Charlie Gréboval

Ulrich Nguétchuissi Noumbé

Audrey Chu

Yoann Prado

Adrien Khalili

Corentin Dabard

Tung Huu Dang

Silviu Colis

Julien Chaste

Abdelkarim Ouerghi

Ulrich Nguétchuissi Noumbé

Jean- Francois Dayen

Emmanuel Lhuillier

Gate Tunable Vertical Geometry Phototransistor based on Infrared HgTe Nanocrystals

Keywords: HgTe nanocrystal, infrared, photodiode, gate effect, mixed dimensionalities device

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HgTe nanocrystals (NCs) combining the semimetal nature of the bulk 1,2 and quantum confinement 3- 5 , presents a unique spectral tunability in the infrared range. 6 Beyond material absorption, HgTe NCs have been used for their IR light emitting properties [7][8][9][10][11][12] as well as for their short 13,14 and mid wave 15,16 IR photoconduction properties. 17 This has led to the demonstration of focal plane arrays operating in the short- [START_REF] Gréboval | Cond-Mat Physicsphysics[END_REF][START_REF] Chu | [END_REF] and mid-wave infrared. 20 Among possible device geometries, the vertical diode is the one that leads to the highest performance so far. The in-built electric field allows zero bias operation reducing the dark current as well as the noise. However, the number of structures that have been proposed to design a vertical geometry diode using HgTe NCs remains quite limited, [21][22][23][24] and does not seem fully optimized. In particular, for an optical band gap in the 500 to 750 meV range, the open circuit voltage is only a few tens of millivolts. This is far smaller than half of the band gap value commonly achieved for PbS quantum dots. Even though a part of this loss may directly be related to the traps in the material, 25,26 it also suggests that the currently proposed diode stack remains sub-optimal.

The design of such diode is nevertheless challenging. Part of the open circuit voltage loss can directly come from the poor doping profile within the diode. Controlling the intrinsic doping in the NC film remains a difficult task and thus it will be of utmost interest to control the film carrier density using electrostatic gates. Field effect transistors based on HgTe films have been reported with various gate technologies such as dielectrics, [27][28][29] electrolytes 30 and even ionic glasses. 31 However, all are based on planar geometry. Implementation of a gate in a vertical geometry appears far more challenging and remains unreported for HgTe NC based diodes.

Our goal is to develop electrodes for the design of infrared NC-based diodes with the dual role of collecting carriers on one hand and controlling the carrier density within the film on the other hand. The development of such electrode faces a second challenge relating to its transparency. In most NC-based diodes, transparent conductive oxides (TCOs) are used. However, in the infrared TCOs present a strong absorption, requiring a decrease in their thicknesses at the cost of an increased contact resistance. Thus, alternative materials should be preferred. Here we explore graphene coupled to LaF3 ionic glass used as substrate and infrared transparent 32 bottom electrode which can also be used to control the carrier density of the NC film. Compared to the works from Yao and coworkers, 33,34 the switch from a conventional dielectric to the high capacitance gate allows us to expand the design of the doping landscape towards higher carrier density.

Coupling infrared NCs 35,36 including HgTe 37,38 to graphene and 2D materials 39 is an approach that stimulated a growing activity over the past few years. So far, the most investigated geometry relies on a planar configuration 13,40 where the graphene is used as a channel of a field effect transistor which is light sensitized by the NCs. 41 The large mobility of graphene is used to generate gain and achieve very large responsivities (i.e. light to current conversion). However, the lack of band gap in graphene comes with a large dark conductance partly balancing the gain benefit. Here, we go further while exploring the use of the graphene large quantum capacitance. Contrary to metal or TCO electrodes, graphene does not screen the electric field induced by the LaF3 ionic glass. As a result, the gate below the 2D material can be used both to control the work function of the electrodes 13,42,43 and to tune the carrier density within the NC film over its surface.

In this work, we demonstrate that exploiting the electrostatic transparency across mixeddimensional hetero-interfaces allows to use the back gate as a knob to control the current flow within the diode. The gate bias enables us to modify the band profile in the NC junction, that can now be switched from n-p configuration to a n + -n-p configuration which is more favorable for charge extraction. This work confirms that HgTe NC-based diode performance can be further improved by optimizing the carrier density profile, in particular, on the n-side, as well as pinpoints this issue as a key element that future work will need to address.

We start by growing HgTe NCs absorbing in the extended short wave infrared using Keuleyan's procedure. 44 The particles (later called HgTe 4k) present a clear excitonic feature at 4000 cm -1 (≈0.5 eV or 2.5 µm), see Figure 1a. The nanocrystals have a planar tripodic shape according to transmission electron microscopy (see Figure 1b). The nature of the majority carriers is also a central parameter for the following material integration and this can be probed using field effect transistor measurements. The latter is designed from electrodes onto a LaF3 substratre which is an ionic glass. 45 LaF3 provides a high capacitance 31 (0.4 µF.cm -2 ) while being all solid-state (i.e. without the constrains of electrolyte). Under such condition, the channel of HgTe NCs shows an ambipolar behavior (Figure 1c) with both hole and electron conductions. The minimum of conductance occurs for a small negative gate bias (VGS=-2 V) meaning that there is a small inherent n doping in this material. This picture is consistent with photoemission measurements on this material, which demonstrate that the Fermi level is close to the middle of the band gap and lies slightly closer to the conduction band. The bottom electrode of the diode made of graphene was also characterized independently (ie without the capping HgTe NC layer). The graphene is a CVD-grown graphene which has been transferred onto the LaF3 substrate. As expected for graphene, we also observe an ambipolar behavior (Figure 2a) for this material under gate bias application, with a minimum of conductance corresponding to the Dirac point observed for VGS= -4 V. The graphene is then patterned as stripes, all connected to a gold contact, see Figure 2b. Using Raman mapping of the 2D mode of graphene (Figure 2c), we check that stripes are well defined. The processing of graphene electrode under stripes allows simultaneous charge collection, while leaving part of the film in direct contact with the gate to further enhance the carrier density tunability within the NC film.

Map of the intensity of the graphene in 2D Raman mode of graphene for the electrode deposited on LaF3. On this map the substrate is brown while the graphene is yellow green

We then design the diode according to the scheme of Figure 3a. A thin (35 nm) ITO layer is deposited on one side of a double side polished LaF3 substrate. The latter will be used as IR transparent gate electrode. The LaF3 substrate provides two functionalities: an IR transparent bottom substrate and a high capacitance gate medium. In LaF3, the gating results from F -vacancies displacement, optimal operating condition is in the 200-250 K range (220 K is used as operating in the following of the paper). Above 250 K the leakage in the gate are high and compete with the channel flow, while below 180 K, the vacancies freeze and the gate tunability is lost. On the other side of the substrate, the CVD-grown graphene is transferred and patterned as stripes, see Figure 2b andc. The absorbing layer is made of a 300 nm film of HgTe 4k (i.e. presenting a band gap at 2.5 µm). On top of the HgTe 4k film, a thin layer of HgTe 7k (i.e. with a band-edge at 7000 cm -1 or 0.87 eV) is deposited. Finally, a top gold contact is used as a hole extractor.

In HgTe, the strong asymmetry of effective mass between the valence and the conduction bands makes that most of the quantum confinement occurs in the conduction band. As the result of the heavy mass of the hole, the valence band is poorly affected by the confinement (i.e. the valence band weakly shifted when confinement is introduced) and it makes that various sizes of HgTe NCs present quasi resonant valence band. 22 The layer of HgTe 7k NCs with a larger band gap (7000 cm - 1 or 0.87 eV) on top of HgTe 4k is used as a unipolar barrier 22 preventing electron diffusion towards the top electrode, while leaving the photo-holes flow.

To confirm the effect of the gate, we measure the current flow through the diode while the gate bias is tuned (the equivalent of a transfer curve in a field-effect transistor), see Figure 3b. Under a gate bias application, we observe a clear modulation of the current, typically by one order of magnitude. This confirms that the gate electrode can be used to tune the carrier density in the vicinity of the graphene electrode. The band profile associated with this diode structure at 0 V is given in Figure 3e. The slightly smaller work function of graphene (4.4-4.5eV) compared to HgTe 4k [START_REF] Chu | [END_REF]22 (4.6-4.7 eV) induces a downward band bending for HgTe 4k at its interface with graphene, while the trend is opposite at the HgTe7k/gold interface. Under positive gate bias application, the n-type nature of the HgTe 4k NC thin film is reinforced creating a n + np band profile which is expected to ease hole and electron extraction, see Figure 3f. On the other hand, when a negative gate bias is applied, holes are injected and a pnp band profile is generated, see Figure 3d. In this case a very poor photo-charge extraction is anticipated.

These predictions are experimentally confirmed by measuring the photocurrent spectrum, see Figure 4a. We clearly observe that the gate bias drives the magnitude of the photocurrent while the bias over the diode is kept constant. No photoresponse is observed while the diode is operated in the pnp configuration. We also clearly observe an enhancement by a factor ≈4 of the photocurrent magnitude as positive gate bias is applied.

The gate effect is quantitatively better monitored by measuring the short circuit current (ISC) and the open circuit voltage (VOC), see Figure 3c and IV curves in Figure S5. The pnp regime (VG<0) is characterized by very low performance: VOC<1 mV and weak photocurrent corresponding to responsivity of the order of 50 µA.W -1 @1.55 µm, which is weak compared to best diodes based on graphene/HgTe NCs. 32 As the gate bias is tuned, we observe a change of sign for the VOC and ISC. This confirms the change of nature for the majority carriers from holes to electrons as gate bias is increased. The gate bias where the open circuit change of sign is -4 V matching well with the Dirac point of graphene. For higher gate biases (n + np regime), the open circuit voltage reaches 6 mV, while the current is 10 times higher (R≈0.6 mA.W -1 @1.55 µm) than for negative gate biases, see Our results demonstrate that increasing the doping level of the NC absorbing layer enables an improvement of the diode performance. It also confirms that in current NC diodes the electron extraction is not as favorable as it could be if more strongly n-doped HgTe NCs might be synthetized while keeping the band gap constant. To summarize, gate control is commonly integrated in planar geometries for field effect transistors, but the use of gates in HgTe NC-based photodiodes remains unexplored. Here, we demonstrate the fabrication of a gate tunable photodiode architecture based on HgTe NCs and a mixed-dimensional vertical stack. The combination of high capacitance LaF3 ionic glass and graphene is used as an infrared transparent electrode that allows us to adjust electrostatically the band profile of the NCs absorbing layer after fabrication. We demonstrate that in the floating condition (i.e. without gate), the band profile does not lead to the optimal condition for charge extraction. This work suggests that additional research will be needed to design better n-doped HgTe NCs to obtain optimized photoelectron extraction. Moreover, as demonstrated here on a first device generation, 2D-0D vertical heterostructures reveal a promising system to introduce electrostatic engineering of the diode absorbing layer.

See the supplementary material for information about nanocrystal growth, material characterization, device fabrication and device characterization.

The project is supported by ERC starting grant blackQD (grant n° 756225). We acknowledge the use of clean-room facilities from the "Centrale de Proximité Paris-Centre" and from STnano platform. This work has been supported by the Region Ile-de-France in the framework of DIM Nano-K (grant dopQD). This work was supported by French state funds managed by the ANR within the

22

 22

Figure 1

 1 Figure 1 HgTe infrared nanocrystals. a. Absorption spectrum of the HgTe NCs. b. Transmission electronic microscopy image of HgTe NCs associated with the spectrum of part a. c. Transfer curve (drain current as a function of the gate bias) for a thin film of HgTe NCs used as the channel of a field-effect transistor which gate is made of LaF3 ionic glass.

Figure 2

 2 Figure 2 Graphene as infrared transparent, work function tunable electrode. a. Transfer curve (drain current as a function of the gate bias) for a graphene layer used as a channel of a field-effect transistor which gate is made of LaF3 ionic glass. b. Image of the patterned graphene deposited onto a LaF3 substrate and connected to a gold contact. c. Map of the intensity of the graphene in 2D Raman mode of graphene for the electrode deposited on LaF3. On this map the substrate is brown while the graphene is yellow green

Figure 3

 3 Figure 3 Gate tunable vertical geometry infrared diode. a. Sketch of the gate tunable diode based on the ITO/LaF3/graphene/HgTe4k/HgTe7k/gold stack. b. Current through the diode while the gate bias is tuned (Vdiode= 0.1 V). c. Short circuit current and open circuit voltage for the diode under illumination (λ=1.55 µm -P=2 mW) as a function of gate bias. Band structure of the diode under negative gate bias (part d.), 0 V bias (part e.) and positive gate bias (part f.). Measurements are conducted at 220 K.

Figure 3c .

 3c Figure 3c. Time response of the diode has been measured and found to be fast (<100 ms, setup limited), see Figure 4b.

Figure 4

 4 Figure 4 Infrared detection using the gate tunable diode. a. Spectral response of the gate tunable diode operated under three gate biases, while the diode bias is set to -0.1 V. Curve have been normalized to take into account the amplifier gain. b. Photocurrent under 0 V diode bias and 10 V gate bias while is the illumination (λ=1.55 µm -P=2 mW) is turned on and off. Measurements are conducted at 220K

Investissements d'Avenir programme by Labex Matisse (ANR-11-IDEX-0004-02) and Labex NIE (ANR-11-LABX-0058, and ANR-10-IDEX-0002-02). ANR also fund grants FRONTAL (ANR-19-CE09-0017), IPER-Nano2 (ANR-18CE30-0023-01), Copin (ANR-19-CE24-0022), Graskop (ANR-19-CE09-0026), NITQuantum. AC thanks Agence Innovation Defense for PhD funding.

The authors declare no competing interests.

The data that supports the findings of this study are available within the article and its supplementary material.


B Xu

P Marsik

E Sheveleva

F Lyzwa

A Louat

V Brouet

D Munzar

C Bernhard

Optical Signature of a Crossover from Mott-to Slater-type Gap in Sr 2 Ir 1-x Rh x O 4

With optical spectroscopy we provide evidence that the insulator-metal transition in Sr2Ir1-xRhxO4 occurs close to a crossover from the Mott-to the Slater-type. The Mott-gap at x = 0 persists to high temperature and evolves without an anomaly across the Néel temperature, TN . Upon Rh-doping, it collapses rather rapidly and vanishes around x = 0.055. Notably, just as the Mott-gap vanishes yet another gap appears that is of the Slater-type and develops right below TN . This Slater-gap is only partial and is accompanied by a reduced scattering rate of the remaining free carriers, similar as in the parent compounds of the iron arsenide superconductors.

The insulator-metal transition (IMT) in complex transition metal oxides with strongly correlated electrons near half-filling of the conduction band is a longstanding research topic [1]. In a so-called Mott-insulator the on-site Coulomb-repulsion (U) splits the conduction band into lower and upper Hubbard bands and thus gives rise to a gap in the electronic excitations. A prominent example are the parent compounds of the cuprates, which become high-T c superconductors upon doping [2]. More recently, the layered iridate Sr 2 IrO 4 has obtained great attention as a high-T c candidate but also as an unusual Mott-insulator [3][4][5][6][7][8][9][10][11][12]. It has a relatively weak Coulombinteraction, due to the extended Ir 5d orbitals, but a strong spin-orbit coupling (SOC) that cooperates to induce a Mott-gap. Like the cuprates, it hosts an antiferromagnetic (AF) order which doubles the unit cell and thus can also lead to a splitting of the conduction band. The latter effect dominates for a so-called Slater-insulator for which the gap occurs only below the Néel temperature T N . Such a Slater-type gap has not yet been observed in these iridates, but the origin of the J eff = 1/2 insulating state is debated and it may be close to a crossover between the Mott-and Slater-limits [6][7][8][9][10][11][12][13][14][15][16][17][START_REF] Singh | Evidence of Slater-type mechanism as origin of insulating state in Sr2IrO4[END_REF][START_REF] Hsieh | [END_REF][20].

A transition from a Mott-to a Slater-type insulator thus may be realized when Sr 2 IrO 4 is doped towards a metallic state and the Mott-gap is more rapidly suppressed than the AF order. A promising candidate is Sr 2 Ir 1-x Rh x O 4 for which the decrease of the dc resistivity upon substitution of Rh for Ir is considerably faster than the one of T N [21][22][23]. Several studies have revealed the interesting properties of the IMT in this system [22][23][24][25][26][27][28][29][30][31][32][33][START_REF] Zwartsenberg | Spin-orbitcontrolled metal-insulator transition in Sr2IrO4[END_REF] which in general can be controlled by a change of (i) the band filling, (ii) the strength of the electronic correlations or (iii) the SOC. Whereas Rh should be isovalent to Ir, it has been shown that the smaller SOC of Rh, as compared to Ir, gives rise to a charge transfer between neighbouring Ir and Rh ions, and thus an effective hole doping [22]. A corresponding shift of the chemi-cal potential in Sr 2 Ir 1-x Rh x O 4 was observed by angleresolved-photoemission spectroscopy (ARPES) [22,32] which suggest that the IMT occurs around x = 0.04 [22]. On the other hand, magnetization and neutron diffraction measurements establish that the AF transition temperature decreases more gradually and persists up to x ∼ 0.15 [22,23,[START_REF] Ye | [END_REF][36][37][38][39].

Here we report the optical conductivity across the IMT of Sr 2 Ir 1-x Rh x O 4 . In particular, we detail how the Mottgap of the parent compound evolves with Rh-substitution and gives way to in-gap states and, eventually, a strongly correlated itinerant state. Notably, after the collapse of the Mott-gap we still observe a smaller gap that develops only in the AF state below T N and thus can be associated with a Slater-type gap. These findings confirm that the IMT of Sr 2 Ir 1-x Rh x O 4 is governed by a complex interplay of Coulomb repulsion, spin-orbit coupling and antiferromagnetic correlations.

Sample synthesis and characterization, as well as experimental methods, are described in Ref. [START_REF]details about the characterization of the samples, the reflectivity measurements and the Kramers-Kronig analysis, the Drude-Lorentz fits, as well as[END_REF].

Figures 1(a-e) display the temperature (T ) dependent spectra of the real part of the optical conductivity σ 1 (ω) for the Sr 2 Ir 1-x Rh x O 4 crystals with 0 ≤ x ≤ 0.15 (corresponding reflectivity spectra can be found in Ref. [START_REF]details about the characterization of the samples, the reflectivity measurements and the Kramers-Kronig analysis, the Drude-Lorentz fits, as well as[END_REF]). They span the transition from the Mott-insulator at x = 0 to a metallic state at x = 0.15. The spectra of the parent compound at x = 0 in Fig. 1(a) reveal an optical gap that develops already above room temperature and deepens continuously toward low temperature. At 10 K, it gives rise to a nearly complete suppression of the electronic conductivity below about 0.2 eV. The sharp features below 0.1 eV are due to infrared-active phonon modes. Towards higher energy, the spectra are dominated by a double peak structure with a lower peak around 0.5 eV (α-band) that has been assigned to the transition between the lower and upper Hubbard bands (LHB and UHB) of the half-filled band derived from the J eff = 1/2 states (around the X-point of the Brillouin zone) and an upper peak around 1 eV (β-band) due to transitions from the J eff = 3/2 band to the UHB of the J eff = 1/2 manifold near the Γ-point [5,[START_REF] Moon | [END_REF]44]. Alternatively, the two-peak structure was interpreted in terms of a mixing of optically active excitations between the LHB and UHB of the J eff = 1/2 band with an optically forbidden spin-orbit exciton [4,45]. However, as shown below, this latter interpretation is not supported by the doping dependence of the α-and β-bands. At x = 0, the α-band exhibits a strong red-shift with increasing temperature. It also becomes broader and gains a substantial amount of spectral weight from the β-band. These trends were previously noted and discussed in terms of excitonic and electron-phonon coupling effects, in analogy to those of the parent compounds of the cuprates [START_REF] Moon | [END_REF]46]. Notably, the Mott-gap feature evolves continuously below 300 K without any clear anomaly around T N ≈ 255 K. The above described gap features are still evident in the spectra of the weakly Rh-doped samples with x = 0.02 and 0.04, in Figs. 1(b) and 1(c), respectively. However, the spectral weight of the in-gap states increases rather rapidly and their depletion at low temperature remains increasingly incomplete. Most of the additional in-gap spectral weight originates from the α-band which shows only a moderate red-shift but exhibits a rapid spectral weight loss and has essentially vanished at x = 0.055. This characteristic collapse of the α-band signifies the disappearance of the Mott-gap of the J eff = 1/2 band around x = 0.055. In clear contrast, the β-band evolves rather continuously across x = 0.055 and persists up to x = 0.15. This suggests that it has a different origin than the α-band, in agreement with the assignment given in the previous paragraph. Despite the collapse of the Mottgap around x = 0.055, the low-energy Drude-peak representing the response of itinerant charge carriers remains extremely weak up to x = 0.07. Instead, most of the low-energy spectral weight is contained in a mid-infrared band that is in the following denoted as M -band.

The observed rapid spectral weight loss and collapse of the Mott-gap related α-band associated with the corresponding increase of the low-energy spectral weight, with the eventual formation of a Drude-like peak, is the spectroscopic hallmark of a transition from a Mott-insulator to a strongly correlated metal. The trends are well known from experimental studies of the doping dependent optical response of cuprates [1,[47][48][49]. And, importantly, they are reproduced by calculations using the one band Hubbard model [50][51][52][53]. The computed spectra even display the M -band, that can be qualitatively interpreted using the high U limit of the one Hubbard model, i.e., the t-J model [50,52]. Within this model, the doped holes can be viewed as spin polarons. While the Drudelike peak reflects intraband absorption within the polaron band, the M -band is due to more complicated excited states involving magnons. The energy of the M -band is predicted to scale with the superexchange constant J [50]. In good agreement, since J is about 135 meV in the cuprates [54] and about 60 meV for the present iridate [55], the energy of the M -band in the strongly underdoped cuprates at 0.5-0.6 eV [47,49] is about twice as large as that of the iridates at about 0.25 eV. In addition, the M -band may be influenced by electron-phonon interaction, as described for the cuprates in Refs. [56][57][58]. At very low doping the spectral weight of the M -band is predicted to be larger than that of the Drude component [53]. Clearly, the data are consistent also with this prediction. The suppression of the Drude peak for Sr 2 Ir 1-x Rh x O 4 with x ∼ 0.055 and 0.07 is likely due to a localization of the polarons by structural disorder (e.g., due to the Rh doping), similar as in weakly doped cuprates [48].

The characteristic changes connected with the IMT are further detailed in Fig. 2(a), which highlights that σ 1 (ω) at 10 K increases rather rapidly with Rh-doping below about 0.4 eV, whereas it decreases at a similar rate above 0.4 eV (up to about 1.8 eV). By fitting the σ 1 (ω) spectra with a Drude-Lorentz model (see details in Ref. x = 0 to about 0.75 eV at x = 0.15. The α-peak shows a similar, moderate redshift, but its spectral weight decreases rapidly and vanishes around x = 0.055, marking a sudden collapse of the Mott-gap. On the other hand, the M-peak first appears at x = 0.02 and softens and eventually merges with the Drude-peak around x = 0.15. The D-and M -bands together gain about the same amount of spectral weight as the one lost by the α-and β-bands.

The doping dependent spectral weight redistribution has been further analysed in terms of the quantity, S(ω c ) = ωc 0 σ 1 (ω)dω, calculated for different cut-off frequencies, ω c . Figure 2(d) shows the normalized spectral weight S(ω c , x)/S(ω c , x = 0) for the spectra at 10 K for some representative values of ω c . For the smallest value of 0.2 eV that is well within the gap region at x = 0, the spectral weight increases very rapidly with the Rh content and continues increasing up to x = 0.15. For the higher cut-off frequencies, this increase becomes less pronounced until at ω c = 2 eV there is no more obvious change. This confirms that the IMT mostly involves electronic excitations below 2 eV.

Next, we focus on the gap formation of the x = 0.07 sample that occurs right below T N and thus seems to be of the Slater-rather than the Mott-type (a similar trend occurs for the x = 0.055 sample). Figures 3(a) and (b) show representative σ 1 (ω) spectra well above, around and well below T N ≈ 180 K and the corresponding difference plots, respectively. The low-energy part of the spectrum at 300 K is composed of a prominent M -band with a broad maximum around 150 meV and a weaker and fairly broad Drude-response (that is superimposed by several sharp phonon modes). In the paramagnetic state, between 300 and 200 K, the spectral weight of the M -band and the Drude-peak increases by a moderate amount. This additional low-energy spectral weight is accumulated from a broad energy range above 0.4 eV and the overall shape of the spectra is characteristic of the response of a bad metal [59]. To the contrary, when going from T N to T = 10 K << T N a gap-like feature appears that involves a partial suppression of the conductivity in the range from 40 to 160 meV. Most of the missing spectral weight is transferred above the gap edge where the conductivity is enhanced up to about 400 meV. A smaller part is shifted to low energy, i.e., < 40 meV, where it contributes to a narrowed Drude-peak. These spectral changes below T N are characteristic of the formation of a partial energy gap in the electronic excitations with a magnitude of 2∆ ≃ 160 meV. Similar trends have been reported for other materials with an AF order that involves spins of itinerant charge carriers. A prominent example of such a spin-density-wave (SDW) material are the parent compounds of the iron arsenide superconductors [60][61][62][63].

The analogy with a partial SDW gap state is further substantiated by a fit with a Drude-Lorentz model. Figure 3(c) shows for the 10 K spectrum (blue line) that a good fit (red line) is obtained with the sum of a Drudeterm (light-blue line) and two Lorentz-oscillators (orange line) that represent the contributions of the Mand β-bands. The temperature evolution of the obtained parameters in Fig. 3(d) confirms that the spectral weight and the scattering rate of the Drude-response exhibit clear anomalies at T N . Whereas the Drude weight slightly increases between 300 and 200 K, it suddenly starts to decrease below T N , at 10 K it is reduced by about 30% as compared to the value at T N . Likewise, the scattering rate of the free carriers decreases more strongly below T N than above T N . The orange sym- bols in Fig. 3(d) show that a similar amount of spectral weight, as the one lost by the Drude-peak, is gained below T N by the incoherent part of the spectrum in the energy range between 100 and 500 meV. This confirms that, similar to the iron arsenide parent compounds, the SDW gap below T N leads to spectral weight transfer from low energy to the region above the gap edge. The enhanced conductivity at very low energies arises from the strong reduction of the scattering rate of the free carriers of the remaining parts of the Fermi-surface. Next, we compare in Fig. 4(a) the temperature evolution of the low-energy spectral weight (normalized to the value at 300 K) from x = 0 to 0.15. For x ≤ 0.04 it confirms that the gap formation evolves without any clear anomaly across T N . At x = 0.055, the spectral weight is almost temperature independent above T N ≈ 200 K, but below T N it decreases noticeably. This shows that just as the Mott-gap collapses the AF correlations start to contribute to the gapping of the low-energy excitations. Moreover, it suggests that the Mott-type and Slater-type mechanisms are cooperative. The most pronounced anomaly around T N is seen at x = 0.07, where the low-energy spectral weight increases at first between 300 and 200 K before it suddenly starts to decrease below T N ≈ 180 K. The increase of the low-energy spectral weight at T > T N together with the absence of an αpeak confirm the complete suppression of the Mott-gap at x = 0.07. The crossover from a Mott-type to a Slatertype gap thus occurs around x = 0.055. At x = 0.15 the low-energy spectral weight increases continuously toward low temperature, as expected for a correlated metal. No sign of a gap formation is seen here down to the lowest temperature and frequency measured.

Below the lower limit of our measurement of ∼ 10 meV, there may still be a pseudogap, as it has been observed in ARPES experiments [22,32]. Indeed, the dc resistivity data [START_REF]details about the characterization of the samples, the reflectivity measurements and the Kramers-Kronig analysis, the Drude-Lorentz fits, as well as[END_REF] are consistent with a decrease of the conductivity below ∼ 10 meV. A weak localization of (some of) the charge carriers can also be the reason why the IMT in the transport data occurs close to x = 0.07, rather than at the collapse of the Mott-gap around x = 0.055. Finally, note that the free carrier response in the metallic state at x = 0.15 in Figure 1(f) is strongly temperature dependent. With decreasing temperature it gains a large amount of spectral weight from the β-band. The unusually high energy scale of this spectral weight redistribution is evident from the graph of the spectral weight difference, ∆S(ω) = S(ω, 10K) -S(ω, 300K), in the the inset of Figure 1(f). It reveals a steep rise of ∆S(ω) below about 200 meV, due to the spectral weight gain of the Drude-response, that is followed by a more gradual decrease that continues up to about 1.5 eV, above which the spectral weight is almost compensated. A weaker structure around 0.7 eV arises because the spectral weight loss of the β-band is accompanied by a rather large red-shift of about 100 meV. Notably, the inverse spectral weight shift is observed for the insulating samples at x < 0.055 for which the spectral weight of the β-band increases as the Mott-gap grows and depletes the in-gap states at low T . The direction of the spectral weight redistribution between the β-band and the low-energy excitations changes around x = 0.07. For this particular doping, the spectral weight shift is limited to a much lower energy scale on the order of the Slater-gap. While we do not have a conclusive explanation of this remarkable trend, it indicates that the itinerant charge carriers at x = 0.15 remain strongly correlated [64].

On the basis of the above described results and their similarity to those of the cuprates and the results of Hubbard model based calculations, we have arrived at the schematic representation of the doping dependence of the low energy density of states of Sr 2 Ir 1-x Rh x O 4 shown in Fig. 4(b).

In summary, we studied the temperature-and dopingdependence of the optical conductivity of Sr 2 Ir 1-x Rh x O 4 crystals with 0 ≤ x ≤ 0.15. In particular, we showed how the Mott-gap vanishes and how the in-gap states and eventually a correlated metallic state emerge with increasing Rh-doping. Moreover, we found that, just as the Mott-gap collapses, a second kind of gap appears that develops only in the AF state and thus is of a Slater-type. Our findings suggest that the IMT in Sr 2 Ir 1-x Rh x O 4 undergoes a crossover from a Mott-to a Slater-type as controlled by the delicate interplay between electronic correlations, spin-orbit coupling, and antiferromagnetic order. Finally, in the metallic state at x = 0.15 the Drude-response is also rather unusual since its spectral weight is strongly temperature dependent with an underlying spectral weight transfer that involves a large energy scale of about 1.5 eV and thus is indicative of the persistence of strong correlation effects.

Figure 1 .

 1 Photon energy (eV)

4 Figure 2 .

 42 Photon energy (eV)

  Photon energy (meV)

Figure 4 .

 4 Figure 4. (color online) (a) Temperature dependence of the low-energy spectral weight showing the progression of the gap formations at 0 ≤ x ≤ 0.07 and the coherent metallic response at x = 0.15. Vertical dashed lines denote TN . (b) Schematic diagram of the electronic states near the Fermi level (EF)for Sr2Ir1-xRhxO4. At x = 0, a Mott-gap occurs in the halffilled J eff = 1/2 band whereas the J eff = 3/2 is fully occupied. Rh-doping of x = 0.02 and 0.04 produces in-gap states. At x = 0.07, the Mott gap has collapsed but the states near the Fermi level are still partially suppressed by a Slater gap that is induced by the antiferromagnetic order. Finally, at x = 0.15, a correlated metal appears.

We acknowledge valuable discussions with A. Georges. Work at the University of Fribourg was supported by the Schweizerische Nationalfonds (SNF) by Grant No. 200020-172611. A. L. and V. B. acknowledge financial support from the French National Agency ANR-15-CE30-0009-01 SOCRATE.


Alex Louat

Benjamin Lenz

Silke Biermann

Cyril Martins

François Bertran

Patrick Le Fèvre

Julien E Rault

Fabrice Bert

Véronique Brouet

ARPES study of orbital characters, symmetry breakings and pseudogaps in doped and pure Sr 2 IrO 4

I. INTRODUCTION

Most Mott insulating oxides display orbital degrees of freedom beyond a non-degenerate half-filled singleorbital model 1,[START_REF] Maekawa | Physics of Transition Metal Oxides[END_REF] . These degrees of freedom complicate the analysis, as they open the possibility of various types of orbital orderings. Even in a seemingly classical example of a Mott insulator such as V 2 O 3 , the orbital occupations change at the metal-insulator transition [START_REF] Park | [END_REF]4 . In layered perovskites, like ruthenates, there are three partially filled t 2g orbitals, creating a hidden one-dimensional character despite the tetragonal structure. Namely, chains of d xz orbitals run along k x (and respectively d yz chains along k y ), which may trigger nesting instabilities 5 . An exception are cuprates, where a half-filled d x 2 -y 2 band at the Fermi level describes the electronic structure quite well. Recently, Sr 2 IrO 4 has become another possible example, because the spin-orbit coupling quite efficiently splits the three t 2g bands into a half-filled non-degenerate J ef f = 1/2 band and two filled J ef f = 3/2 bands 6,7 , called hereafter J 1/2 and J 3/2 . The geometry of the J 1/2 band is rather unusual, with strongly entangled spin and orbital characters.

J ±m J 1/2 = |d yz , ∓σ ± i|d xz , ∓σ ± |d xy , ±σ √ 3 ( 1
)
where σ is the spin and m J the pseudospin. This J 1/2 character was confirmed experimentally 8,9 . Sr 2 IrO 4 thus realizes new low-energy Hamiltonians which may exhibit new forms of magnetic ordering (see for instance Ref. 10).

In this paper, we use angle-resolved photoemission spectroscopy (ARPES) to check directly the orbital character of the bands approaching the Fermi level in Sr 2 IrO 4 . This is possible thanks to selection rules associated to the light polarization, which modulate the intensity of the bands, depending on their symmetry with respect to mirror planes of the structure 11 . We uncover a strong polarization dependence of the ARPES intensity, which seems counter-intuitive at first, as J 1/2 has a very isotropic shape by construction. We explain through explicit density functional theory (DFT) calculations that a J 1/2 band on the Sr 2 IrO 4 lattice should indeed exhibit a well defined k-dependence of the orbital character that is in very good agreement with our findings. This "hidden" orbital degree of freedom is often forgotten and places Sr 2 IrO 4 at an intermediate situation, between cuprates and ruthenates. It could play a role in subtle symmetry breakings reported in iridates, either a time-reversal symmetry breaking in pure Sr 2 IrO 4 12,13 or density waves in doped compounds 14,15 . We carefully take into account these intensity modulations to discuss possible intrinsic changes in the dispersion along equivalent directions of the Brillouin Zone (BZ), both for the pure and Rh-doped Sr 2 IrO 4 . We conclude that they are identical within at least 50 meV.

The possible role of hidden orders in the formation of arXiv:1907.01247v1 [cond-mat.str-el] 2 Jul 2019 pseudogaps has been much discussed, especially in the case of cuprates 16 . In iridates, two different kinds of pseudogaps have been reported. In electron doped systems, obtained by La 17 or surface 18 doping, the Fermi surface emerges from the M point (equivalent to the nodal point in cuprates), which may mean there is a pseudogap at the X point, similar to hole-doped cuprates. Theoretical calculations have discussed the possible emergence of a pseudogap due to strong antiferromagnetic fluctuations 19,20 . In hole-doped iridates, which can be obtained by Ir/Rh substitutions 21 , the Fermi surface emerges around the X points 22,23 . A k-dependent pseudogap was first reported 22 , implying some type of undefined symmetry breaking. In contrast, we have found a pseudogap over the entire Fermi surface (FS) 23 , rather suggesting that it is a characteristic of the metallic state itself.In this paper, we clarify that the pseudogap-like features strongly depend on the experimental conditions, especially on polarization. This very likely explains the different conclusion of references 22 and 23 . We further show that at the X point spectral weight from unoccupied states leaks in and causes a leading edge in the electron distribution curve (EDC) at ∼ 30meV, which is independent of the experimental conditions. This finally gives a solid basis to analyze the pseudogap-like behavior in this particular case.

To compare dispersions and lineshapes between theory and experiment, we use an oriented cluster extension of dynamical mean-field theory (DMFT) 19 . This technique has recently been applied successfully for pure and electron-doped Sr 2 IrO 4 19,24 . We present here results for the hole doped case, which simulates Rh doping. The Fermi surface and dispersions of all bands are in remarkable agreement with ARPES experiments. We do not find a pseudogap on the hole pockets, but intensity does extend to the X point. We then suggest that the pseudogap-like feature is associated with disorder due to in-plane Rh substitutions, which is not taken into account in the calculations.

II. ORBITAL CHARACTER IN Sr2IrO4

A. Polarization dependent ARPES measurements Fig. 1 (a-c) displays Fermi surfaces measured at 50K in Sr 2 IrO 4 doped with 15% Rh, at 100eV photon energy, with different polarization and orientation. The inten- Direct and folded bands are plotted as solid and dotted lines, respectively. The t2g orbital character obtained from the calculation is displayed using a three-color (RGB) scale : dxz in red, dyz in green and dxy in blue. In (c) and (d), the decomposition of the orbital character for the top band along ΓX2 is indicated, without and with spin-orbit, respectively. In (e), the orbital weights for the same band in the J 1/2 , J 3/2 basis are indicated.

sity modulations we are going to describe are however common to all dopings of Sr 2 IrO 4 . The intensity at X is due to the J 1/2 band and is found stronger for X points along k y in (a), along k x in (b) and along the diagonal in (c), where the sample is rotated by 45 • . Obviously, different polarizations "favor" different X points, which implies a symmetry breaking that is not immediately expected from the equation given above for J 1/2 .

Well known selection rules 11 state that orbitals odd (resp. even) with respect to a mirror plane will be detected with polarization odd (resp. even) with respect to that plane. The geometry of our experiment is sketched at the bottom of the figure. The light polarization A lies along the y axis in linear vertical (LV) polarization and within the xz plane in linear horizontal (LH) polarization (these sketches correspond to normal emission (k x =0), the angle of A to the sample surface will change for higher k x , see supplementary 25 ). In LV, A is odd/xz and even/yz, so that orbitals odd/xz are expected to be detected along k x and orbitals even/yz along k y . The strong difference in intensities along k x and k y strongly suggests that we have bands even/yz along k y (favorable case) and even/xz along k x (unfavorable case). This is the case for d yz (even/yz) and d xz (even/xz), respectively. On the other hand, for LH, A is even/xz, while both components are present with respect to yz 25 . While the interpretation of this situation is not as straightforward, the fact that the strongest intensity is now along k x confirms that an orbital even/k x dominates in this direction.

We also observe a strong variation of intensity as a function of k x (more than a factor 10 between k x =1 and k x =3), indicating that the cross section increases when A is almost perpendicular to the surface (towards grazing incidence). This means that the orbitals at X must have a strong out of plane component, which is the case for d xz or d yz .

If we now turn the sample by 45 • , the selection rules apply with respect to the plane containing the diagonal of the unit cell (ΓM) and the sample normal (this is not a true mirror plane, because of the oxygen positions). There is no difference anymore between the spots along k x and k y , as expected for d xz and d yz which are equivalent with respect to this diagonal plane.

B. Calculated orbital weights within DFT

To understand the expected orbital characters observed around the X point, we calculate the k-resolved spectral function and project it at each k-point on the local Ir 5d-orbitals to get their orbital weights. In Fig. 2, we show the Kohn-Sham band structure of Sr 2 IrO 4 calculated within the local density approximation (LDA) [START_REF]To distinguish dxz and dyz orbitals easier, we introduced a small orthorombicity in the structure (space group then becomes Fddd (70)[END_REF] along ΓX 2 MΓ without spin-orbit coupling (SOC) in (a) and with SOC in (b). the calculation was performed using the WIEN2k software [START_REF] Blaha | WIEN2K: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties[END_REF] .We use as color scale the weight of each orbital d xz (red), d yz (green) and d xy (blue) obtained from this calculation and normalized by the total Ir weight. There is significant hybridization (nearly 50%) with oxygen, but this does not affect the band symmetry. There is also significant hybridization with d x 2 -y 2 around Γ 28 , that does not enter the color scale.

There are two sets of t 2g bands because of the 2 Ir per IrO 2 plane (see Fig. 1), with the two Ir orbitals in-phase or out-of-phase 25 . We call the first ones direct bands and write them (d xz , d yz , d xy ) [solid lines in Fig. 2(a-b)], and the second ones folded bands (d xz *, d yz *, d xy *) [dotted lines in Fig. 2(a-b)]. The distinction between them is made simply by comparison to the bands of a non-distorted structure 7 . It is important to take this into account for ARPES measurements, as the two types of bands have opposite parities with respect to a ΓX mirror plane 25 and the folded bands have typically a much weaker intensity 29 . There is an additional doubling of the number of bands because of the two planes per unit cell, which gives a "bilayer splitting", which is usually small in Sr 2 IrO 4

25 , but it is clearly visible for the bands near -1eV at Γ for example.

In Fig. 2(c-e), we show explicitly the orbital character of the topmost band along ΓX 2 . Without SOC, it is nearly of pure d yz character and meets a band of nearly pure d xz character near Γ and X 2 . At these points, the orbital character cannot be individually defined since the bands are degenerate. The SOC mixes the orbital characters [Fig. 2(d)] and the colors of Fig. 2(b) are indeed not as clear as in (a), but they are still dominated by one component in many places. One actually obtains a doublet of J 1/2 character, as defined in Eq.( 1), and a degenerate quartet of J 3/2 character, only when the SOC acts on three degenerate t 2g states. While the three t 2g orbitals are nearly degenerate in Sr 2 IrO 4 at the atomic level 9 , this is not the case for the Bloch states at a given k point. For instance, at the Γ point, the bands of character d xz * and d yz * are degenerate at 0.3eV, but the d xy * band is much lower around -0.5eV. Consequently, the character of the topmost band is mixed between d xz and d yz , with an admixture of only 10% d xy /d x 2 -y 2 instead of 33% expected for a "standard" J 1/2 state. The situation is slightly different at X 2 since the d yz * band lies near the Fermi level while the energy of d xz * band is circa -1.0eV. As a result, the character expected near X 2 along k x is now 70% d yz * for the topmost band. Note that the SOC acts only between bands of same nature (direct or folded) and is ineffective between direct and folded bands. Therefore, it does not lift the degeneracy between the bands of d xz / and d yz * character. As the situation is reversed near X 3 along k y (where the topmost band is of 70% d xz * character), the character of the whole band is in average over the Brillouin Zone essentially J 1/2 but at most of the k-points, and notably at the X points, the character may be far from the standard (1/3,1/3,1/3) decomposition. This is confirmed in Fig 2(e) where we plot the orbital character of the topmost band along ΓX 2 with respect to the J 1/2 and J 3/2 basis. The topmost band is on average composed of 80% of J 1/2 character and of 20% of J 3/2 character along this direction, which is in good agreement with the decomposition given in Ref. 30.

The ARPES observation that a well-defined t 2g orbital character persists at X (also used recently in ref. 31) is then in agreement with the calculation. Introducing correlations beyond DFT will modify slightly the relative ratio of the decomposition at each k-point. First, correlations enhance the spin-orbit polarization 32,33 , which brings the J 3/2 band at Γ below the Fermi level. Second, they open a gap at X in Sr 2 IrO 4 to form an insulator.

III. COMPARISON TO DMFT CALCULATIONS

We now compare our data to a dynamical mean-field theory (DMFT) calculation, which captures both the gap opening and the correct position of J 3/2 compared to J 1/2 . In Fig. 3, we show a calculation for the hole doped case in which within the J 1/2 band the hole density is n h = 12%. To treat the J 1/2 band within the calculation, we use an oriented cluster extension of DMFT, which has recently been applied successfully for pure and electrondoped Sr 2 IrO 4 19,24 . Going beyond single-site DMFT by including spatial fluctuations to treat the J 1/2 band is essential to obtain a correct spectrum in the paramagnetic phase. The J 1/2 spectrum is then supplemented by the DMFT spectrum of the J 3/2 manifold. This assumes that the J 3/2 spectrum does not change much upon hole doping due to its completely filled character, except for an additional energy shift due to the change in chemical potential. We use an effective on-site Coulomb interaction of U eff = 0.6eV as in the electron-doped case discussed in Ref. 19.

We have used different polarizations and geometries to measure all Ir bands of Rh-doped Sr 2 IrO 4 from -2eV to the Fermi level E F 25 . The experimental dispersions (solid lines) are overlayed in Fig. 3(a) onto the calculated spectral function. They compare well, in particular the J 3/2 bands and the J 1/2 band features close to the Fermi level are well captured. Deviations seem to occur at the bottom of the J 1/2 band, which is higher in the calculation. Comparing to the original DFT calculation shows that this is not due to a renormalization of J 1/2 induced by correlation. The problem is probably due to an inaccurate extraction of the experimental dispersion in this region, where two bands overlap 25 .

Comparing the calculated Fermi surface in Fig. 3(b) to the experimentally observed spectrum (Fig. 1) shows good agreement and motivates a detailed investigation of the spectrum. In the following we focus on the spectrum at the high symmetry point X 2 , as well as at the Fermi vector k F along the path Γ-X 2 . Within the calculation, we have to choose a broadening η of the spectral function. A value of η = 0.08 leads to good agreement with experiment, but hides some of the FS features that become apparent at small broadening only. There, as in the electron-doped case 19 , the Fermi surface is composed of two sheets due to the two different directions of antiferromagnetic fluctuations that are included via our cluster treatment.

As can be seen in the top panel of Fig. 3(c), the spectral function at X 2 has a peak above E F , as expected for a hole pocket around X. In the bottom panel of Fig. 3(c), we simulate the energy distribution curve (EDC) signal based on this data via f FD T (ω) • A(k, ω), where f FD T (ω) denotes the Fermi-Dirac function. The low energy tail of the spectrum gives the impression of a tiny peak at E F after multiplying with f FD T (ω). The spectrum is quite different at the Fermi energy for k F . For the realistic broadening used in our calculation, the spectrum is relatively flat around E F , see top panel of Fig. 3(c), but it has an underlying two-peak structure. After multiplying with the Fermi-Dirac distribution, the curve at k F shows a peak close to E F , but below. This should not be confused with a pseudogap, as the leading edge of the spectra (used experimentally to define the pseudogap 25 ) is still defined by the Fermi edge.

IV. IMPACT OF THE INTENSITY MODULATIONS ON THE ARPES LINESHAPES

The polarization dependence of the ARPES intensity we have described is not only important to better understand the orbital structure of J 1/2 , but also because it strongly affects the intensity of the spectra and sometimes their shape. We will show that it is particularly important to take this into account to analyze pseudogaplike features around the X point.

A. Comparison of the dispersions along kx and ky

Figure 4(b) sketches the spectral function with its intensity modulations along the Γ -X 2 -Γ path. First, the dominant orbital along ΓX 2 will be d xz , which have very different intensity in most experimental conditions compared to d yz along ΓX 3 (see intensity modulations in Fig. 1). Second, this dominantly d xz band joins at X 2 with a dominantly d yz * band. These two bands are even with respect to the ΓX mirror plane 25 , so that they should have similar intensity under the same polarization, but the intensity of the d yz * band is intrinsically much weaker due to its folded character 29 . When the gap opens at X 2 , both the d xz /d yz * and direct/folded characters get mixed. The expected modulation of intensity along Γ -X 2 -Γ is illustrated by the size of the markers.

In the bottom part of Fig. 4, we compare the dispersion along three different ΓX paths for pure Sr 2 IrO 4 [Fig. 4(df)] and Rh-doped Sr 2 IrO 4 [Fig. 4(h-j)]. The distribution of intensity is very different along ΓX 3 (d) and Γ X 2 (f), for example, which follows well the expectations of Fig. 4(b). The intensity concentrates on the direct band, i.e. on the sides of the dispersion for (d) and at the center for (f). In Fig. 4(e), the intensity is more equally distributed between the center and the sides, which is not expected from the direct/folded difference alone [(d) and (e) should be equivalent in that respect] and could be due to the contribution of d xy or imperfect selection rules. This nevertheless validates the existence of strong intensity variations near X.

Besides these intensity variations, the dispersions themselves look different at first sight. They seem to extend closer to E F in (d) and (h). For the Rh case, it even looks as if there was no gap along k y (h) and a real gap along k x (i). Indeed, their leading edges at k F [see Fig 4(c)] are quite different, with an onset at larger energies for X 2 (35meV) than for X 3 (12meV). This could indicate a charge-density-wave-like gap opening along k x and questions the equivalence of k x and k y . To compare the dispersions more precisely, we overlay the same white curve over all images, just shifted up by 0.25eV for the Rh case, which is the estimated difference in chemical potential between the pure and the Rh-doped sample 34 . It is quite clear that the intensity is slightly outside this curve in (d) and (h) and inside in (e) and (f), suggesting again a truly different dispersion. This is illustrated more quantitatively by the momentum distribution curve (MDC) spectra taken at -0.4eV for the pure case [Fig. 4(g)] and -0.05eV for the Rh case [Fig. 4(k)]. In both cases, the peaks are found at slightly different positions along k x and k y with δk=0.06*ΓX. The dispersion through k y along Γ'X 2 looks however even more different, with peaks shifted towards X. This implies that a difference between k x and k y would not be a sufficient explanation.

Two types of origins can be considered to explain such differences. It could be intrinsic due to a real splitting of the dispersion. As different experimental conditions may pick up different contributions of the two bands, this would lead to different peak positions. This splitting could be due to 1D fluctuations, as in the oriented cluster DMFT calculation described before, or other types of order, as the d-wave spin-orbit density wave 33 . The energy shift of the white curve needed to produce the observed splitting in momentum is of the order of 50meV. Alternatively, or additionnally, there could be an extrinsic contribution due to the intensity modulations. Such modulation may distort the lineshapes by giving different importance to contributions coming from different k points. As we know that there is indeed a strong intensity modulation around X, we give particular attention to this point. The most striking feature of the MDC in Fig. 4(g) and (k) is actually that they are very asymmetric, distorted towards the center. Although a lorentzian is normally expected for a MDC curve 11 , it is quite commonly distorted towards the occupied side of the band 35 . This can be un- derstood as due to the integration of the tails of all EDC located at neighboring occupied k points. We show in supplementary that the change in intensity as a function of k described before can indeed satisfyingly explain the different shapes of MDC observed for the pure case. As the simulation depends both on the intrinsic shape of the spectral function (its width as a function of k for example, which is a priori unknown) and on the details of the extrinsic variation of intensity, we cannot simulate quantitatively the spectra. Therefore, we cannot exclude an intrinsic variation of the dispersion coexisting with this extrinsic modulation, with an upper bound of 50meV, however. This is not negligible, but the broad linewidths (0.23eV for the pure case shown in Fig. 4(c) for example) do not allow to refine this further. On the other hand, this is already incompatible with the splitting of 0.2eV at X considered by Ref. 33 as a sign of d-wave spin-orbit density wave order. We note that such a splitting was also unclear in the raw data of Ref. 17 and may be an artifact of the fitting procedure used in this paper.

The case of Rh is more tricky as the band is now above the Fermi level at X and one would not expect a strong contribution to the lineshape from this unoccupied part. However, just like there is a remaining intensity at X coming from the tail of the spectra above E F in our calculation in Fig. 3(c), there could be a sizable contribution in this case. Comparing with the spectra of the pure compound shifted up to the expected position for Rh (i.e. by 0.25eV, like the white dispersion) indeed suggests that some intensity can be expected at X. In this case, modulation of the relative intensity at k F and at X could affect the lineshape and possibly change the leading edge shape. We now take a closer look at this point.

B. Addressing the question of the pseudogap in Rh-doped Sr2IrO4

A pseudogap is usually defined as the position of the leading edge of the spectra closest to E F in one particular direction. In Fig. 1, we indicate by the dotted red circle the k points of such spectra and, in Fig. 5 (a-c), we build images with spectra taken along this contour. The full EDC spectra for the different ΓX directions are presented in supplementary. The leading edge is indicated by a cross. Values ranging from nearly zero to 60meV are found. It is clear that they are not associated to the different X points, but to the experimental conditions, as they change at a given X point for different experimental conditions. The tendency is to measure a larger pseudogap when the intensity is higher, wherever it occurs in k-space. Further analysis is clearly needed to understand what should be called a pseudogap in this case.

The ARPES study of Ref. 22 concluded that the pseudogap was different on the "direct" and "folded" parts of the Fermi Surfaces, forming "Fermi arcs" instead of hole pockets around X [see Fig. 1(d)]. This point is quite important to check, as it would completely change the FS topology. We note that the equivalence between the two sheets is dictated by periodicity of the 2 Ir unit cell itself, so that this proposal is quite puzzling. In Fig. 5(d), we track the position of the leading edge along the hole pocket at X 2 in the ΓM-LH FS. We choose this case because the two sides have relatively similar intensities in this geometry. The leading edges of the spectra in Fig. 5(d) are remarkably constant around -60meV. This rules out a specific pseudogap on the folded FS compared to the direct one. The different pseudogaps measured by Ref. 22 are more likely due to different intensities on the two sheets in their measurement conditions, as for ΓX 2 and Γ X 2 in Fig. 4(c).

Interestingly, all spectra show the same leading edge at X [Fig. 4(c)], despite the very different absolute intensities (more examples are given in supplementary 25 ). However, their onset is located around -30meV from E F , which is unexpected and anomalous for a metal. This defines a new energy scale to characterize this pseudogaplike behavior, independently of experimental conditions. As there are equal contributions of d xz /d yz and direct/folded bands at X, it indeed makes sense that this measurement is less sensitive to the experimental conditions. On the contrary, the leading edge value measured at k F is directly related to the relative intensity between X and k F . From our previous study of the pure case, we have seen that the relative intensity at X is strongest along Γ'X 2 , then ΓX 2 and finally ΓX 3 . This explains perfectly the trend of a larger leading edges onsets along Γ'X 2 (45meV), then ΓX 2 (35meV) and finally ΓX 3 (12meV).

This shifts the discussion from the pseudogap-like fea-ture to the meaning of this new energy scale at X. The intensity around X is incoherent, in the sense that there is no quasiparticle (QP) peak that could be defined anywhere with a width smaller than its binding energy. In the case of Rh, the disorder may enhance scattering between different k values. This would naturally explain why our calculations, which do not include any disorder effects, do not reproduce the experimentally observed leading edge position of the EDC at a non-zero binding energy.

V. CONCLUSION

Using polarization-dependent ARPES, we have directly determined the orbital character of the bands in Sr 2 IrO 4 . Despite the band dispersion being well described by the J 1/2 picture, the band closest to the Fermi level has -at a given k point -well-defined orbital character in terms of cubic harmonics. This is in line with ab initio calculations and attaches great importance to anisotropies and orbital degrees of freedom. From a conceptual point of view this observation has an interesting consequence: the coefficients of an expansion of the J 1/2 Wannier orbital in terms of cubic harmonics aquire k-dependence. This prevents the corresponding band from being spanned by a simple tight binding model with atomic J 1/2 orbitals. It is rather reminiscent of the Zhang-Rice construction in cuprate systems 36 , where the Wannier orbital of dominant d x 2 -y 2 character is obtained as a superposition including p x and p y orbitals with kdependent coefficients.

In the ARPES experiment, the k-dependent orbital variations give rise to strong matrix element effects that modulate the intensities. Because of the k-dependence of the J 1/2 Wannier orbital itself the assumption of slowly varying matrix elements breaks down. In addition, the presence of two transition metal atoms per unit cell, which is a rather common situation, imposes strong selection rules. As a consequence, dispersions measured in equivalent directions of the Brillouin zone sometimes appear different. We considered both intrinsic (e.g. symmetry breakings) and extrinsic (e.g. matrix elements) origins for these differences. Although we cannot exclude the former, with an upper bound of 50meV to shifts or splittings that could be present in the electronic structure, we show that the strong modulation of ARPES intensity by matrix elements observed here is already able to explain most of these differences.

In Rh-doped Sr 2 IrO 4 , we show that the leading edge of the spectra detected throughout the FS, commonly used to define a pseudogap, strongly depends on the experimental conditions. However, at the center of the hole pocket -a k point which is not part of the Fermi surface -spectral weight is observed with a leading edge of 30meV, independently of experimental conditions. This establishes a new energy scale defining this highly anomalous metallic state.

We have performed theoretical calculations within the recently developed oriented cluster dynamical mean-field scheme, which was already applied to electron doped Sr 2 IrO 4 . Here, we show that it also provides a good description of the dispersion of hole-doped Sr 2 IrO 4 . We provide a detailed comparison between the polarized ARPES measurements and the calculated spectral function. In theory, the leading edge at the Fermi surface does not show a depletion of spectral weight. We speculate that disorder effects, associated with Rh substitutions, are responsible for creating the spectral weight at X and the pseudogap-like feature. Rh-doped Sr 2 IrO 4 appears as an interesting example of disordered correlated metal that deserves further studies.

More generally, our study indicates ways to better characterize pseudogap-like features with ARPES. Depressions of spectral weight at E F have indeed been observed in many correlated systems. Besides the famous example of cuprates, one dimensional systems 37 , aperiodic crystals 38 , "bad metals" like manganites, nickelates and others 39 all tend to show a depression of intensity at the Fermi level. It is likely that all these behaviors do not have the same meaning and significance, but more precise definitions are lacking. A common feature of these situations is to exhibit broad lineshapes in energy and momentum. We emphasize in our study that this makes them sensitive to rapid intensity modulations and that non-lorentzian MDC lineshapes are a signature of such a situation. In this case, the simple estimation of the pseudogap by the leading edge value becomes insufficient and a full study of the intensity distribution is necessary.

Figure 1 .

 1 Figure 1. (a-c) Fermi Surface for 15% Rh doped Sr2IrO4 at 50K in different experimental conditions : Linear Vertical (LV) polarization with ΓX oriented along x (a), Linear Horizontal (LH) with ΓX oriented along x (b) and LH with ΓM oriented along x (c). The polarization A is indicated by the red arrow and the dotted red circle indicate the k positions of the spectrum closest to EF in this BZ. (d) Sketch of the Fermi Surface with hole pockets around X point having predominantly dxz or dyz character. Thin parts are folded with respect to the 2 Ir Brillouin zone [blue square, see also (g)]. (e-f) Geometry of our experiment for LV (e) and LH (f) configurations. (g) Sketch of the in-plane unit cell with the two Ir atoms and the ΓX mirror plane (blue circles represent oxygen atoms).

Figure 2 .

 2 Figure 2. Kohn-Sham band structures of Sr2IrO4 within DFT-LDA without (a) and with (b) spin-orbit coupling.Direct and folded bands are plotted as solid and dotted lines, respectively. The t2g orbital character obtained from the calculation is displayed using a three-color (RGB) scale : dxz in red, dyz in green and dxy in blue. In (c) and (d), the decomposition of the orbital character for the top band along ΓX2 is indicated, without and with spin-orbit, respectively. In (e), the orbital weights for the same band in the J 1/2 , J 3/2 basis are indicated.

J 1 / 2 :J 1 / 2 :J 1 / 2 :J 1 / 2 : 2 MJ 1 / 2 :Figure 3 .

 121212122123 Figure 3. (a) Extracted experimental dispersions (color lines) superimposed on an oriented cluster DMFT calculation with U=0.61eV and a hole density of n h = 12%. Experimental dispersions were extracted in 15 %Rh doped Sr2IrO4 and the raw data are shown in the supplementary. The colors are mainly there to follow the bands more easily and are just loosely connected to J=1/2 (one red band, the other band is above EF ), J=3/2 (green) and dxy/d x 2 -y 2 (blue). (b) Corresponding Fermi surface for a broadening of η = 0.08. The third quadrant shows the FS for η = 0.03. (c) Spectral function A(k, ω) and energy distribution curves fFD(ω) • A(k, ω) around the Fermi energy at X2 and kF along Γ -X2 as indicated by stars in (b).

Figure 4 .

 4 Figure 4. (a) Sketch of the Fermi surface of Rh-doped Sr2IrO4 and positions of the different cuts represented below. (b) Sketch of the band structure along the path Γ-X2-Γ'. Thin lines represent the dxz and dyz* dispersion, before mixing. To simulate the gap opening, we assume a potential of 0.3eV along ΓX. The resulting dispersion is shown with markers having orbital character as color scale and weight as size (the direct band is assumed arbitrarily to have 10 times the weight of the folded band). (c) Energy distribution curve (EDC) spectrum for Rh doped sample at X (top) and kF (bottom) for different ΓX directions. A reference spectrum at X for the pure case is shown in black with its abscissa (top) shifted by 0.25eV. This corresponds to the shift observed between the pure and Rh compound in the images (d-j). (d-f) Dispersion in Sr2IrO4 measured using LH polarization along ΓX3 (d), ΓX2 (e) and Γ'X2 (f). The thin white line is a guide to the eye (the same in each case). (g) Momentum distribution curve (MDC) spectra at -0.4eV for the (d-f) cuts. (h-j) Same dispersions for 15% Rh doped Sr2IrO4 measured in the same experimental conditions. The white dispersion is shifted up by 0.25eV. (k) MDC spectra at -0.05eV sample for the three cases (h-i).

Figure 5 .

 5 Figure 5. (a-c) Leading edge spectra images taken along the circular contour, indicated as dotted red lines in Fig. 1(a-c). Red crosses indicate the position of the leading edge. (d) Leading edge spectra image around the X2 point of the ΓM-LH FS in Fig. 1.


Zeineb Ben Aziza

Hugo Henck

Debora Pierucci

Mathieu G Silly

Emmanuel Lhuillier

Gilles Patriarche

Fausto Sirotti

Mahmoud Eddrief

Abdelkarim Ouerghi

van der Waals Epitaxy of GaSe/Graphene Heterostructure: Electronic and Interfacial Properties

Keywords: Van der Waals heterostructures -GaSe, graphene -Molecular Beam Epitaxy -RHEED -XPS, ARPES -Band structure -Raman spectroscopy -Charge transfer

Stacking two-dimensional (2D) crystals in so-called van der Waals heterostructures, like the combination of 2D-layered GaSe and graphene, provides the ability to obtain hybrid systems which are excellent candidates to design novel nanoelectronic and optoelectronic devices. Here, we report the electronic and structural properties of the direct large scale growth of few GaSe layers by Molecular beam Epitaxy (MBE) on graphene/SiC. RHEED images showed sharp streaky features indicative of atomically flat GaSe films grown via a van der Waals epitaxy (vdW). Micro-Raman spectroscopy showed that, after a van der Waals heterointerface formation, the Raman signature of pristine graphene is preserved. However, the GaSe growth tuned the electronic properties of graphene by shifting the Dirac point by about 80 meV toward lower binding energies with respect to the π-band of pristine graphene, attesting an electron transfer from graphene to GaSe. ARPES measurements showed that the maximum of the valence band of few layers GaSe are located at the Γ point at a binding energy of about -0.73 eV relative to the Fermi level (p-type doping). From the ARPES measurements, a hole effective mass defined along the ΓM direction and equal to about m*/m0 = -1.1 was determined.

By coupling the ARPES data with XPS measurements, the Schottky interface barrier height was estimated to be 1.2eV. These findings about interlayer interactions and electronic structure of 2D heterostructure represent a key issue for the new devices concepts.

Graphene is a single layer of carbon atoms arranged in honeycomb lattice. Despite graphene high carrier mobility, the absence of a band gap limits its application in the field of optoelectronics 1 . From here comes the importance of exploring the interaction with other 2D materials, in particular with the family of artificially structured materials such as transition metal dichalcogenide (TMDCs like MoS2) and semiconducting metal monochalcogenide (GaSe, InSe) 2,3,4,5 . The stacking of layered materials on top of each other permits the creation of novel functional materials and promises tunable optoelectronic properties for future devices with improved functionalities 1,6,7 .

GaSe is a van der Waals layered material, possessing a strong in-plane vs out-of-plane electronic conduction anisotropy which results from highly anisotropic bonding forces 8 . The atoms in unit of atomic tetra-layer (TL) i.e. Se-Ga-Se-Ga: TL, have strong bonds and all bonds are saturated on TL surface. Moreover, the 2D-TLs are stacked in the out-of-plane direction via weak inter-TLs van der Waals interactions. The layered hexagonal GaSe was chosen to be the optical active material because of its high photoresponsivity (2.8 AW -1 ) and high external quantum efficiency (≈1300%) that were recently demonstrated 5 . As grown GaSe is a p-type semiconductor, this p-type character provides a major property because in the 2D family most of the TMDCs are n-type 9 . Moreover, GaSe has a direct bandgap of about 2.1 eV, for a number of layers greater than seven [10][11][12] . The two minima of the conduction band can both be populated by photoexcited carriers. The radiative recombination, associated with the direct and the indirect gaps, may occur simultaneously. This makes GaSe a promising material for optoelectronic applications 5,13,14 . The GaSe based optoelectronic devices cannot only be used as photodetectors and THz source generator 15 , but also for the nonlinear optical applications 16 due to its large nonlinear optical coefficient (54 pmV -1 ). Various methods have been reported to grow GaSe thin films, including chemical vapor deposition 17 , pulsed laser deposition 18 , and molecular beam epitaxy 19,20 (MBE). Apart from early pioneering works 19,20 there are a few works on the MBE growth of atomically thin epitaxial GaSe on insulating substrates and they are mainly focusing on the electronic properties. Indeed, they focus on the structural properties, and on the optical emission properties of epitaxial single and few-layer GaSe grown on sapphire and silicon by MBE 4,21 .

Therefore, we demonstrate in this work a novel approach to assemble GaSe with epitaxial graphene/SiC; this paves the way for the realization of a well-ordered GaSe/graphene based heterostructure. The synthesis of multilayer intrinsic p-type GaSe is obtained by molecular beam epitaxy (MBE) on n-type epitaxial graphene on SiC(0001). This approach enables the growth of large area vertical p-n junction van der Waals heterostructure. Compared to the conventional heterojunctions of 3D materials, this 2D heterojunction has several advantages. First, the combination of epitaxial graphene/SiC (chemical inert surface and massless-Dirac conduction) with the MBE growth of GaSe (with intrinsic gap) allows a full control at the atomic scale of the vertical thickness of the heterostructure with an almost perfect interface. Moreover, the absence of the Fermi-level pinning at the atomically sharp heterointerfaces, offers a unique opportunity to realize devices with gate-tunable characteristics 22 . This study is focused on understanding the electronic structure of GaSe as well as the interlayer coupling between GaSe and graphene. The understanding of the interface physics at the atomic scale is a challenging issue for the design of new devices with more functionality.

In particular, RHEED was employed to control both the in-plane axis epitaxy alignment of GaSe film with respect to the graphene substrate and to control the crystalline quality during the growth. Micro-Raman spectroscopy was conducted to explore the vibration frequencies of phonons corresponding to the characteristic vibrational modes of layered GaSe on epitaxial graphene. After GaSe/Graphene heterointerface formation, the shifts observed in the Raman spectra of graphene layer reveal that a charge transfer has occurred between the p doped few layers GaSe and the n doped graphene. ARPES was used to investigate the electronic properties of GaSe i.e. the GaSe band structure and also the position of the valence band maximum relative to the Fermi level. This information coupled with the work function measurements by high resolution x-ray photoemission spectroscopy (HR-XPS) allows determining the Schottky barrier height (SBH) at the GaSe/graphene heterostrucutre.

Results and discussions:

Thermal decomposition of SiC(0001) can be used to produce large graphene films with a long-range order and high electron mobility 23 . Monolayer, bilayer, and few-layer graphene on SiC are obtained by tuning different experimental parameters (temperature, annealing times, and thickness of the SiC substrate) 24 . The graphene used in this study was obtained by annealing 6H-SiC(0001) at 1550 °C in an Ar atmosphere (see methods). The sample was divided into two parts, the first is considered as a reference and will be named hereafter "pristine graphene", and the second has been used for the growth of few layers GaSe. The details of the growth are outlined in methods section.

Layered GaSe has planar TL character with in-plane hexagonal lattice and multi-stacked TLs along the c-axis with a relatively weak interlayer coupling, enabling its isolation down to a single TL. Each atomic TL consists of four covalent bonds, with an in-plane lattice constant of 0.37 nm and a TL thickness of about 0.8 nm 25,26 . Schematics of GaSe/graphene hybrid system and the top view of the in-plane GaSe hexagonal crystal structure are shown in Figure 1(a).

Figure 1(b) presents the RHEED image of pristine graphene/SiC. Figure 1(c) show the RHEED pattern of GaSe film deposited on epitaxial graphene. Graphene and GaSe display in-plane hexagonal symmetry with hexagon's sizes of aGaSe =0.374 nm and of aGraphene = 0.247 nm. The appearance of the sharp elongated streaks in the RHEED patterns, in early stage of the growth of GaSe film until the end of the growth process, suggests a well-crystallized order and flat surface of GaSe epilayer. Figure 1(c) shows that the presence of two streaky-lines pattern (two periods indicated by red and blue arrows) and they are correlated with in-plane <1-100>-axis and <11-20>-axis of in-plane hexagonal GaSe. Two main orientations of the GaSe domains are observed from the nucleation phase (in the early first GaSe TL coverage regime) as we illustrate in a scheme drawing in Figure 1(d) with aligned triangular GaSe islands on graphene (with a 180°-twinned ones) together with their ~ 30° rotated islands apart. From RHEED images in Figure 1(b) and (c), we extracted the large lattice mismatch between GaSe and graphene that is equal to -12.6% for GaSe domain aligned with the underlying graphene and of + 51.4% for the 30° rotated domains. This hybrid 2D-layered material/Graphene interface is often understood to be formed through van der Waals forces 20 and does not involve covalent bonding 9 . Often two in-plane domain orientations of 2D materials growth on graphene are mentioned, particularly by molecular beam method, without understanding if its origin is related to the kinetics of the growth or to the presence of defects on the surface of graphene (even for very low density) 27 .

One additional advantage of graphene as a supporting substrate for GaSe is to promote the GaSe growth at lower substrate temperatures (200 -250 °C). The ability to decrease the growth temperature of such 2D materials represents a big advantage for large scale device manufacturing in particular for applications where heterogeneous integration with graphene devices is required.

To study the interface structure and chemical compositions at the local scale of the GaSe/graphene heterostructures, we have carried out scanning transmission electron microscopy (STEM) and selective area electron diffraction (SAED) studies. We then used micro-Raman spectroscopy to probe the effects of the presence of GaSe on the vibrational and electronic properties of graphene. A typical Raman spectrum of bulk GaSe consists of characteristic peaks for the A 1 1g mode, E 1 2g mode, E 2 1g mode, and A 2 1g mode. The two A1g modes correspond to the out-of-plane vibrational mode of the Se-Ga-Ga-Se lattice, while E1g and E2g are associated with the in-plane vibrational mode. Figure 3(a) shows the Raman spectra performed with a 532 nm laser wavelength in different positions of the sample.

We notice the presence of three of GaSe characteristic peaks, where the most prominent Raman mode corresponds to the A 1 1g mode at 132 cm -1 . The Raman vibrational modes at E 1 2g at 206 cm -1 , and A 2 1g at 307cm -1 are weak with small peak intensities. Moreover, the E 2 1g Raman peak around 260 cm -1 is almost due to the reduction in the scattering centers for E1g mode so that the Raman scattering for this mode becomes less effective 29,2 . These spectra confirm what was reported for decreasing peaks intensities with reducing layer thickness 30 . The number of peaks together with their respective intensities indicate that the grown GaSe film is multi-layered 21,31,3 . Figure 3(b) shows a representative Raman spectrum of GaSe/graphene in the wavelength range 1300-2800 cm -1 . Numerous spectra were acquired in different areas of the substrate in order to check the uniformity of the signal. These spectra exhibit the three main peaks expected for graphene samples: i) D band at 1355 cm -1 , ii) G band at 1595 cm -1 and iii) 2D band at 2705 cm - 1 . The D peak is barely visible, indicating the high quality of pristine graphene. Moreover, the intensity of this peak does not increase after the GaSe growth suggesting that the formation of the heterostructure did not induce defects in the graphene underlayer.

Since the 2D and G bands positions are strongly dependent on the charge carrier concentration; they are used as probe of the graphene doping level. In order to better resolve the G peak of our spectra a background subtraction was done i.e. the spectrum of the SiC substrate (before the graphitization process) was used as reference and subtracted from the graphene one. In our GaSe/graphene heterostructure, we observe a clear upshift of the 2D mode. Since in our Raman measurements the spectra were taken at room temperature and the laser power was low enough to avoid the influence of laser heating, the observed 2D band upshift does not originate from strain induced by temperature gradients. Hence, this upshift of the 2D peak indicates a decrease in the electron concentration in graphene i.e a decrease of the n-type doping of epitaxial graphene on SiC induced by the GaSe layers. This phenomenon indicates that when graphene contacts GaSe, a dipole layer is formed at the interface due to electron transfer from graphene to GaSe 32 .

Furthermore, the G peak presents a downshift of about 3 cm -1 in the case of GaSe on graphene which can give us a more quantitative estimation of the hole doping. Based on the formula 𝜔 𝐺 -1580 = |𝐸 𝐹 | × 42 𝑐𝑚 -1 𝑒𝑉 -1 linearly linking the G peak energy to the Fermi level [33][34][35] , we estimate a decrease in the graphene Fermi level of about 80 ±5 meV attesting a decrease in the n-type doping of graphene. From the corresponding Fermi energies, we calculate the variation in the doping level of graphene thanks to the following relation between the doping density N and the Fermi level EF: |𝐸 𝐹 | = ℏ𝑣 𝐹 • √𝜋|𝑁|. For a Fermi velocity equal to 𝑣 𝐹 = 1.1 × 10 6 𝑚/𝑠 36,37 , we obtain an electron doping density for the pristine graphene |𝑁|~ 1.6 × 10 13 𝑐𝑚 -2 which decreased to |𝑁|~ 1.1 × 10 13 𝑐𝑚 -2 for the GaSe/graphene heterostructure. Therefore, the hole doping density induced to graphene is found to be equivalent to ∆|𝑁|~5× 10 12 𝑐𝑚 -2 . Similar behavior was also observed with 2D CdSe nanoplatelets and epitaxial graphene, where a much larger electron transfer from graphene to CdSe was demonstrated so that graphene switched from n to p type character 38 . It is worth noting that the alteration of the G mode Raman frequencies caused by eventual strain could not be completely excluded but in this case the shift of the G peak should be in the same direction as the shift of the 2D peak 39 i.e. a shift toward higher frequencies. To calculate the charge transfer, we considered the downshift of the G peak; it could be underestimated in presence of strain 40 .

HR-XPS measurements were carried out to uncover the electronic properties and ensure the stoichiometric of the GaSe/graphene heterostructure. The XPS spectra recorded under surface sensitive conditions hν = 60 eV for Ga 3d and hν = 100 eV for Se 3d are shown in Figure 4(a) and (b), respectively. The spectra were analyzed using the curve fitting procedure described in Methods. The binding energies (BEs) of the Ga 3d5/2 and Se 3d5/2 core levels are 19.8 eV and 54.7 eV, respectively 41 . These values are in good agreement with others reported on thin-film and bulk single-crystal 19,42 . In both spectra, there is no signature of other bonds 43 In Figure 5(c) the measured band structure was compared with theoretical calculation of bulk GaSe of X. Li et al. 31 . Due to the fact that the sample is formed of two GaSe domains at 0° and 30°, we superimposed to the ARPES spectrum the dispersion along the ΓM direction (Figure 5(c)) and the ΓK direction (Figure S1) of the bulk GaSe Brillouin zone (BZ). The measured band structure along the ΓM direction presents a good agreement with the theoretical calculation as shown in Figure 5(c). The dispersion along the ΓK direction illustrated in Figure S1 shows that some of the bands along this direction are also visible and results from the presence of two GaSe domains. This result proves the high quality of the grown GaSe on top of graphene/SiC as well as the unaffected band structure of GaSe within our van der Waals heterostructure 8 . In particular as expected for a bulk GaSe, the maximum of the valence band (VBM) is located at the  point, ensuring that the number of TL GaSe presents on the sample are greater than seven 31 . In fact as the number of layer decrease (less than 7 TL) the VBM splits in a symmetric way along the  point, and the band gap pass from direct to indirect, demonstrating an opposite behavior compared with TMDCs 44,45 .

We have also determined the effective mass of the hole close to the  point of the BZ along the M high symmetry directions. The experimental dispersion has been fitted with a parabolic model 𝐸(𝑘) = 𝐸 0 + ℏ 2 2𝑚 * 𝑘 2 where m* is the effective electron mass and ħ is the reduced Planck constant. We found that the hole effective mass at the  point is about m*/m0 = -1.1±0.1, see Figure 5(d) where the dispersion fitting used to calculate the effective mass is illustrated. One can notice that this mass is close to m0 which implies that the GaSe band is poorly dispersive suggesting a very limited mixing of the valence band 46 . Furthermore, this calculated effective mass obtained at room temperature along the M direction is nearly twice the in-plane mass calculated for GaSe at low temperature (at 10K) 11 . This difference could be explained by the fact that the effective mass is anisotropic and hence varies greatly with the measurement direction.

According to the above values from XPS and APRES measurements, we are able to figure out the band offsets resulting from the junction formation. In fact, one of the most determining properties of a metal-semiconductor interface is its Schottky-barrier height (SBH), which is a measure of the mismatch of the energy levels for the majority of carriers across the metalsemiconductor interface. In the case of p-doped few TL GaSe /n-doped graphene heterostucture, the lack of dangling bonds on both surfaces implies the absence of surface states. Moreover, no bonds are present at the interface between the two materials, i.e. the heterostructure is held only by van der Waals interactions. Alike a standard metal-semiconductor interface, the particular properties of these vdW heterostructure ensure the formation of a quasi-ideal (semi) metalsemiconductor interface with a behavior approaching the Schottky limit where the SBH is given by the difference between the metal work function (𝜙 𝑚 ) and the electron affinity (𝜒) of the semiconductor 47 . In our case the pristine graphene is n-doped and presents a work function of 4.30 eV. The few TL GaSe present a p-type doping and a measured work function of 4.70 eV (i.e. an electron affinity of 3.4 eV 42 considering a band gap of 2.1 eV [48][49][50] ). At thermal equilibrium the Fermi level in the two materials must be aligned. The charge flow from the graphene to the GaSe, as confirmed by the Raman measurements, leads to the formation of a dipole layer at the interface. In the GaSe an accumulation region is formed followed by a downwards band bending.

Then the SBH formed at the interface is given by:

𝑆𝐵𝐻 = 𝐸 𝑔 -(𝜙 𝑚 -𝜒) = 1.2 𝑒𝑉
Based on this calculated value, the band alignment diagram of the GaSe/graphene heterostructure is derived and shown in Figure 6. The measurement of this SBH is of fundamental importance to the successful design of any semiconductor device as it controls the electronic transport across the metal-semiconductor interface. In particular, thanks to the extreme low reactivity of these hexagonal two dimensional layered structures, we managed to obtain a p-n junction between a (semi)-metal and a semiconductor in which the interface operates close to the Schottky limit. Moreover, the tunability of graphene work function, e.g. by electrostatic doping 51 can be exploited to adjust the graphene Fermi level to the GaSe conduction band minimum to reduce or completely remove this Schottky barrier at the interface.

Concerning this point, the MBE growth process of the GaSe on graphene ensures a high purity growth and a high control of the number of TL allowing to easily change the thickness of the heterostructure from few TL to one TL. This is a huge step forward in the all 2D metalsemiconductor junction engineering, because by reducing the GaSe thickness to one TL we are able in principle to induce a vanishing of the depletion region and a total collapse of the Schottky barrier creating an Ohmic contact.

Another highly interesting aspect of our method was the p intrinsic doping of the GaSe few TL on n doped graphene. Theoretical studies have predicted that the band gap of the GaSe may be widely tuned by varying the numbers of layer in the crystal or by inducing mechanical strain 52,31 . The GaSe/graphene/SiC structure is of particular interest because the stepped surface of graphene/SiC substrate is expected to produce a periodic strain or auto-organisation of monolayer/bilayer graphene 53 that is strictly mechanical in nature, as well as a charge modulation beneath the GaSe. This modulation is a result of confinement, with a significant one-dimensional (1D) or two-dimensional (2D) lateral potential modulation induced by the nanofacet of the graphene substrate 54 . These effects can be exploited to induce tunable band gaps in GaSe electronic structure with the hope of making practical 2D materials devices.

Conclusions:

In summary, we demonstrate the molecular beam epitaxial growth of hybrid graphene/SiC (0001) heterostructure via van der Waals epitaxy process. Even though the lattice mismatch between GaSe and graphene is at least 12.6 %, the heterostructure is commensurate, epitaxial growth is reached with well-defined crystalline GaSe films in spite of a two in-plane GaSe rotated domains. GaSe induces a decrease in the charge density of the graphene underlayer.

ARPES measurement reveals the GaSe electronic structure: the Fermi level position indicates a p-type doping and theVBM is located at the  point, as expected for a bulk-like GaSe band structure (i.e. number of TL greater than seven). Combining ARPES results with work function measurements, the Schottky barrier height at the GaSe/graphene of the heterostructure was determined. This successful synthesis of few layered GaSe on large area epitaxial graphene substrate can pave the way to broaden the use of 2D GaSe crystals as excellent candidates for optoelectronic applications with high photoresponse and FET characteristics.

Supporting Information:

Section I: Sample preparation and characterization methods. Section II: Comparison between the measured band structure and the theoretical calculation of bulk GaSe along the ΓK direction (Figure S1). This materials is available free of charge via the Internet at http://pubs.acs.org.

Competing financial interests:

The authors declare no competing financial interests.

  Figure 2(a) shows a typical low magnification STEM image of 2D GaSe/graphene. The STEM image indicating the 2D layered crystals are preferentially oriented in the c-axis direction. This image indicates that the 2D GaSe film is structurally uniform and highly crystalline.Figure 2(b) shows a typical STEM image a high resolution of the GaSe with clear hexagonal lattice structure along the caxis. The lattice spacing is measured as 0.4 nm, as expected for the hexagonal GaSe along the (0001) axis (insert figure2(b)). The interlayer separation between the graphene underlayer and the GaSe was about 0.33 nm. This interlayer distance was in agreement with that for vdW heterostructure28 . The composition of the GaSe layer was studied by Energy Dispersive X-ray Spectroscopy (EDX) mapping as shown in figure2(c) and 2(d). The specially resolved EDX elemental mapping of the Ga and Se show relatively uniform distribution, indicating composition uniformity across the films. The EDX images demonstrate a high crystalline and continuous film of GaSe, in which the Ga and Se atomic range could be identified. The results clearly show the presence of a sharp interface without inter-diffusion between GaSe and graphene layer. Interestingly, the GaSe layer exhibits a homogenous chemical composition. The EDX spectra revealed that the 2D film consist of Ga and Se with an atomic ratio of 1:1.

  (i.e. oxygen or carbon), indicating that the GaSe crystal are not contaminated. The work function of pristine graphene and few TL GaSe were also determined via the measurement of the low energy cutoff of the secondary electron (SE) energy distribution curve obtained by XPS measurements at a photon energy of hν = 100 eV (Figure 4(c)), see method. A value of 4.30 eV ±0.05 eV is found for the pristine graphene, and 4.70 ± 0.05 eV with the few TL GaSe. We used angleresolved photo electron spectroscopy (ARPES) to study the band structure of the GaSe films on epitaxial graphene. Figure 5(a) illustrates the valence band structure of few TL GaSe around the  point of the first Brillouin zone (BZ) using an excitation energy hν = 60 eV. In order to get better clarity of the bandstructure, the second derivative of the photoelectron intensity as a function of energy and k-momentum, is shown in Figure 5(b). The zero binding energy (i.e, the Fermi level) is taken at the leading edge of a clean metal surface in electrical contact with the heterostructure.

Acknowledgements:

  This work was supported by the H2DH grants. We acknowledge support from GANEX (Grant No. ANR-11-LABX-0014) and Labex "Nanosaclay (Grant No. ANR-10-LABX-0035)". GANEX belongs to the public funded Investissements d'Avenir program managed by the French National Research Agency.

Figure captions : Figure 1 :

 :1 Figure captions:

Figure 2 :

 2 Figure 2: (a) and (b) Bright-field Scanning Transmission Electron Microscopy (STEM) image of GaSe/graphene heterostructure, high resolution STEM image place in the inset, the (c) (d) EDX elemental maps showing the spatial distribution of Ga and Se, respectively.

Figure 3 :

 3 Figure 3: a) The characteristic peaks for different locations on GaSe grown on graphene, the spectra are exactly the same indicating substrate-independent growth with similar crystal quality owing to the vdW of 2D materials; b) Comparison of micro-Raman spectra taken on the pristine graphene (black color) and GaSe/graphene (red color) layers on different locations of the sample.

Figure 4 :

 4 Figure 4: (a) and (b) Ga 3d and Se 3d core level XPS peaks of few layers GaSe grown on graphene. No reaction with the substrate is observed and the positions and line shapes of the Ga 3d and Se 3d peaks indicate Ga-Se bonding. (c) Secondary electron cut-off vs. kinetic energy referenced to the Fermi level to determine the work function of pristine graphene and GaSe/graphene heterostructure. The experimental data points are displayed as dots. The solid line is the envelope of fitted components.

Figure 5 :

 5 Figure 5: ARPES measurements of bulk GaSe on epitaxial graphene heterostructure: a) ARPES measurements of GaSe/graphene measured at hν = 60 eV along the ΓM direction of graphene first Brillouin zone, and b) The second derivative of the spectra a) exhibiting a better visibility of the bands. The Fermi level position is located at the zero of the binding energy (marked in blue dotted line). c) Comparison between the measured band structure and the theoretical calculation of bulk GaSe of X. Li et al 31 along the ΓM direction. d) The dispersion fitting used to determine the hole effective mass for GaSe defined along the ΓM direction.

Figure 6 :

 6 Figure 6: Schematic of the GaSe/Graphene band alignment diagram, as determined by XPS core level analysis. Ф and EF denote the work function and the Fermi energy, respectively. Eg is the energy gap.