Ko-Fan Huang

Yuval Ronen

Régis Mélin

Denis Feinberg

Kenji Watanabe

Takashi Taniguchi

Philip Kim
email: pkim@physics.harvard.edu

Interference of Cooper quartet Andreev bound states in a multi-terminal graphene-based Josephson junction

 . The energy spectrum of these CQ-ABS can be controlled by biasing MT-JJs due to the AC Josephson effect 12 . Here, using gate tunable four-terminal graphene JJs complemented with a flux loop, we construct CQs with a tunable spectrum. The critical quartet supercurrent exhibits magneto-oscillation associated with a charge of 4e; thereby presenting the evidence for interference between entangled CQ-ABS 13 . At a finite bias voltage, we find the DC quartet supercurrent shows non-monotonic bias dependent behavior, attributed to Landau-Zener transitions between different Floquet bands 14 . Our experimental demonstration of coherent nonequilibrium CQ-ABS sets a path for design of artificial topological materials based on MT-JJs 15- 18 .

At a normal (N)-superconductor (S) boundary, current is induced via Andreev reflection (AR) [START_REF] Andreev | The Thermal Conductivity of the Intermediate State in Superconductors[END_REF] , i.e., an electron impinging on S binds to another electron near the interface, transmitting a Cooper pair into the S region while a hole is reflected. By constructing two such boundaries one creates an SNS JJ, which can be viewed as an electronic analogue of the optical Fabry-Perot (FP) interferometer. Each boundary acts as an AR mirror and in similarity to the FP, resonances are formed in the junction. In this case, these resonances are correlated electron-hole states, the so-called Andreev bound states (ABSs). Due to Cooper pair condensation, ABSs are manifested as electron-hole pairs while each ABS is degenerate in spin. Extending this coherent transport process between multiple superconducting electrodes, two or more Cooper pairs are entangled across the N-region, forming CQ-ABS (Cooper quartet for two entangled Cooper pairs) [START_REF] Freyn | Production of nonlocal quartets and phasesensitive entanglement in a superconducting beam splitter[END_REF][START_REF] Cuevas | Voltageinduced Shapiro steps in a superconducting multiterminal structure[END_REF][START_REF] Jonckheere | Multipair dc Josephson resonances in a biased all-superconducting bijunction[END_REF][START_REF] Pfeffer | Subgap structure in the conductance of a three-terminal Josephson junction[END_REF][START_REF] Cohen | Nonlocal supercurrent of quartets in a three-terminal Josephson junction[END_REF] or higher order ABS states [START_REF] Yokoyama | Singularities in the Andreev spectrum of a multiterminal Josephson junction[END_REF][START_REF] Riwar | Multi-terminal Josephson junctions as topological matter[END_REF][START_REF] Meyer | Nontrivial Chern Numbers in Three-Terminal Josephson Junctions[END_REF][START_REF] Eriksson | Topological transconductance quantization in a four-terminal Josephson junction[END_REF] .

In a two-terminal JJ, two superconducting phases are introduced. However, only the phase difference 𝜑 between the two terminals is an observable quantity. Hence the spectrum is one dimensional, depending exclusively on 𝜑. When there is a phase difference applied across the junction, by either current or magnetic flux, each populated ABS carries a supercurrent obeying the current-phase relation and the outcome is transferring Cooper pairs from one lead to another. As a barrier is introduced in the junction, a gap is opened between each electronhole pair of equal spin states. Therefore, the energies have a 2π-periodicity with respect to 𝜑 and the ABS spectrum is analogous to a crystal band structure with 𝜑 playing the role of crystal momentum. More generally, the ABS spectrum may span in 2D, 3D or even higher dimensions, solely determined by the number of superconducting contacts on the same junction.

Along with the ability of controlling the number of conducting channels, low superconducting contact resistance and weak back-scattering [START_REF] Allen | Spatially resolved edge currents and guided-wave electronic states in graphene[END_REF][START_REF] Ben Shalom | Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene[END_REF][START_REF] Borzenets | Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes[END_REF] make graphene an ideal choice for exploring MT-ABS physics. Utilizing the tunability of graphene chemical potential, one can modulate the coupling strength at each contact, thereby engineering the ABS spectrum. Our graphene-based MT-JJs use Ti/Al as the superconducting contacts, where Al is chosen owing to its large superconducting coherence length (~1µm). A four-terminal JJ including a superconducting loop is fabricated on graphene-hBN-SiO2 structure as shown in Fig. 1a (additional fabrication information can be found in the Method section).

All measurements were performed at 300 mK. Before we conduct the MT-JJ measurement, we first characterize our device with a two-terminal measurement and the S-loop implements a superconducting quantum interference device (SQUID) geometry. For this measurement, we applied a bias voltage 𝑉 to the loop, via two series connected RC filters and the output current 𝐼 is measured at 𝑆 ! while 𝑆 " is floating. Fig. 1b shows an I-V measurement curve of the junction. In the small bias regime, supercurrent flows in the junction and the bias voltage drops are only on the series connected resistors 𝑅 #$ (200 Ω each) in the filters. As the current exceeds the critical current 𝐼 % of the SQUID, the slope of I-V curve changes suddenly at the corresponding applied voltage 𝑉 % . Since the bias voltage is distributed among two filter resistors and the normal junction resistance, the critical current can be obtained from 𝐼 % = 𝑉 % /2𝑅 #$ . Upon applying the magnetic field 𝐵, 𝐼 % is modulated and exhibits SQUID-like pattern as a result of the two interfering superconducting paths in the loop (blue and red dashed lines in Fig 1a). Fig. 1c shows the differential conductance (𝐺 = 𝑑𝐼/𝑑𝑉) as a function of bias voltage and magnetic field. The higher conductance area near the zero-bias regime (central orange part) is the supercurrent region and its edges mark the value of 𝐼 % . As the magnetic field is swept, 𝐼 % is modulated with a periodicity of 𝛿𝐵 = 145 µT, corresponding to the unit flux quantum 𝛷 & = ℎ/2𝑒 for an enclosed area of 𝐴 = 14.2 µm 2 , matching our device loop size (including the area increase due to London penetration depth). An additional slower frequency ( 𝛿𝐵 ' = 3 mT) originated from the Fraunhofer oscillations is observed, corresponding to an area of 0.69 𝜇m 2 , which agrees with the junction dimensions. We find that the strength of the critical current can also be tuned according to the graphene carrier density via a back-gate voltage 𝑉 () . As shown in Fig. 1d, 𝐼 % decreases monotonically as 𝑉 () approaches the charge neutrality point of graphene located at 𝑉 () ≈ -60 V. Reduction of 𝐼 % close to the Dirac point is expected due to the decreasing number of ABS carrying current in the graphene channels [START_REF] Heersche | Bipolar supercurrent in graphene[END_REF] .

With reconfiguration of the external circuitry, our device can serve as a MT-JJ where the common Nregion graphene channel is proximitized. MT-JJ with magnetic flux loops was studied theoretically and experimentally in bi-SQUID devices [START_REF] Rech | Proposal for the observation of nonlocal multipair production[END_REF][START_REF] Strambini | The ω-SQUIPT as a tool to phase-engineer Josephson topological materials[END_REF] , where the equilibrium (i.e., no potential difference between the junctions) ABS spectrum was investigated. Our fourterminal device geometry with gate-tunable graphene weak link allows us to study biased MT-JJs in the nonequilibrium regime, where the nonlocal CQ can be investigated [START_REF] Mélin | Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction[END_REF] . Moreover, by threading a flux through the device loop we aim to modulate the CQ-ABS spectrum. Fig. 2a shows the measurement scheme adopted in this study for phase sensitive quartet detection. We apply DC bias voltages 𝑉 " and 𝑉 ! to 𝑆 " and 𝑆 ! , respectively, and a small AC bias voltage 𝛿𝑉 to the loop electrodes 𝑆 &* and 𝑆 &( . At given bias voltages, we measure the AC current contribution 𝛿𝐼 " and 𝛿𝐼 ! flowing to 𝑆 " and 𝑆 ! , respectively.

Figure 2b shows the differential conductance measured at 𝑆 " (𝐺 " = 𝛿𝐼 " /𝛿𝑉) as a function of the two DC bias voltages 𝑉 " and 𝑉 ! . We identify four high conductance regions (marked by four white dashed lines crossing at the origin), which correspond to four different supercurrents. For instance, when 𝑆 ! and 𝑆 & are equipotential along 𝑉 ! = 0, a Josephson supercurrent flows between these two contacts carried by a Cooper pair-ABS. Subfigures (i) (ii) and (iii) illustrate these local supercurrents between different pairs of S-contacts. The critical values of the supercurrents can be extracted from the widths of the signals, which are 0.47, 0.42, 0.38 𝜇A, respectively. Similar data can be obtained for differential conductance 𝐺 ! = 𝛿𝐼 ! /𝛿𝑉 measured at S2 (see Section 2 in SI). In addition to the two-terminal Josephson currents (i)-(iii), we observe another supercurrent signal along the 𝑉 " = -𝑉 ! line. This supercurrent is labelled as (iv) Quartet and it is carried by CQ-ABS. The quartet supercurrent is a direct evidence of MT-ABSs in our system due to the fact that all contacts are at different chemical potentials. Similar quartet supercurrent signatures were inferred previously in three-terminal Josephson junctions made from diffusive metal 10 and 1D nanowires [START_REF] Cohen | Nonlocal supercurrent of quartets in a three-terminal Josephson junction[END_REF] . The novelty in our four-terminal JJ device is the presence of a magnetic flux loop, enabling direct probing of the CQ-ABS coherence via magnetic field dependence of the critical current. The left panels of Fig. 3a-b show the quartet differential conductance measured at 𝑆 ! (i.e., 𝐺 ! along the quartet line 𝑉 " = -𝑉 ! ) as a function of the magnetic flux 𝛷 = 𝐵 • 𝐴 measured at different back-gate voltage 𝑉 () . The quartet differential conductance 𝐺 +,",! probes the quartet critical current 𝐼 .% (see Section 5 in SI). As a function of 𝛷, clear oscillations of 𝐺 + are observed, demonstrating periodic modulation of 𝐼 .% (𝛷) due to phase coherence of the CQ-ABS. By taking the Fourier transform of 𝐺(𝛷) (the right panel of Fig. 3 ab), we find two major periodicities 𝛷 & /2 and 𝛷 & , where 𝛷 & = ℎ/2𝑒 . The relative strength of the periodicities is tuned via 𝑉 () . As we discussed in Fig. 1d, 𝑉 () adjusts the number of channels in graphene and the coupling of S-electrodes, thus modifying the ABS spectrum. In particular, at 𝑉 () = 25 V (Fig. 3a), 𝐼 .% exhibits a prominent contribution from 𝛷 & /2periodicity, which, as we show now, provides direct evidence for the charge 4e associated with the CQ-ABS.

The observation of the two periodicities tuned by the gate voltage resembles the SQUID oscillation in Fig. 1c, where the 𝛷 & /2 oscillation would be viewed as the second harmonic of the fundamental quantum flux periodicity. However, the magnetooscillation here in Fig. 3a-b cannot be related to DC-SQUID harmonics since there is only one single junction (between 𝑆 &* and 𝑆 &( ) that is at equal potential. In addition, the bias voltages used in this measurement are in a range where one has AC Cooper pair Josephson currents rather than DC. Furthermore, we carefully delineate our signal from the contribution of finite bias multiple Andreev reflections (MARs) by measuring an oscillatory differential conductance, following the 𝐼 .% (𝛷) variation along the quartet bias condition (𝑉 " = -𝑉 ! ) above the MARs background (see Fig. S3c in SI). By adopting the perturbative approach expanded towards the finite bias regime (see Section 5 in SI for detailed discussion), we find that the modulation of the periodicity is associated with interference of three different contributions to the CQ-ABS: two conventional quartets (3-terminal) and a novel process, the split-quartet (4-terminal). As shown in Fig. 3c (Qa) & (Qb), the two conventional quartets take place among 𝑆 " , 𝑆 ! and only one of the two loop electrodes. In these processes, the entangled Cooper pairs enter the loop either through 𝑆 &* or 𝑆 &( . Since every Andreev reflection picks up the phase of the superconducting contact, these conventional quartet processes acquire phase factors 𝑒 +(0 ! 10 " ) at 𝑆 &* and 𝑒 +(0 ! 10 " 1345/5 # ) at 𝑆 &( , where 𝜑 " (𝜑 ! ) is the phase difference between 𝑆 " (𝑆 ! ) and 𝑆 & . Note that the factor 4 in the exponent reflects that two Cooper pairs depart from the same electrode of the grounded loop. If there were only this type of 3-terminal quartet process in the system, the phase factor at 𝛷/𝛷 & = 0 would become equivalent to that at 𝛷/𝛷 & = 1/2, leading to 𝛷 & /2-periodicity in 𝐼 .% (𝛷).

While the conventional quartet process described above is common in three terminal JJs, the four-terminal JJ with a loop enables a different type of quartet, the split quartet (Fig. 3c (SQab)). In the split quartet process, two entangled Cooper pairs are spatially separated into the two electrodes of the loop, yielding a phase factor 𝑒 +(0 ! 10 " 1!45/5 # ) . The resulting critical current contribution has 𝛷 &periodicity. The modulation of 𝛷 & /2and 𝛷 & -periodic oscillation components in 𝐼 .% (𝛷) at different backgate voltages indicates that the occurrence of the two different types (i.e., conventional and split) of quartet process is determined by the relative contact couplings, which are tunable via gating (see Section 5 in SI).

The quartet supercurrent can also be modulated by the quartet voltage 𝑉 . , which is the actual voltage applied on the junction along 𝑉 " = -𝑉 ! . The variation of 𝐺?𝛷, 𝑉 . A is proportional to that of 𝐼 .% ?𝛷, 𝑉 . A along the quartet line since it is an increasing function of the critical current (see section 5 in SI). Therefore this differential conductance measurement serves as a good indicator to investigate the behavior of quartets as a function of magnetic field and the quartet voltage. Figure 4a shows a 2D color plot of 𝐺 " (the quartet conductance measured at 𝑆 " ) as a function of 𝑉 . and the normalized magnetic flux 𝛷/𝛷 & at a fixed gate voltage 𝑉 () = -5 V, where the quartet current is strong (see Fig. S4 in SI). At a constant 𝑉 . , 𝐺 " (𝛷) exhibits oscillations corresponding to 𝐼 .% (𝛷) with periodicity 𝛷 & /2 and 𝛷 & components as discussed in Fig. 3. Interestingly, we find that the oscillation period and phase of 𝐼 .% (𝛷) are also tunable as 𝑉 . varies. As shown in Fig. 4b, in the low bias regime ( 𝑉 . < 7.2 µV), 𝐼 .% (𝛷) shows predominantly the 𝛷 & -periodic oscillation, in phase with the SQUID phase of equilibrium supercurrent. However, as 𝑉 . increases, 𝐼 .% (𝛷) oscillation becomes predominantly 𝛷 & /2 -periodic near 𝑉 . ≈ 𝑉 +7 ≡ 7.2 µV. Above this critical bias voltage 𝑉 +7 , 𝐼 .% (𝛷) oscillation resumes the 𝛷 & -period, but the phase is shifted by 𝜋 compared to 𝐼 .% ?𝛷, 𝑉 . < 𝑉 +7 A. We note that for this high bias quartet regime (𝑉 . > 𝑉 +7 ), the flux dependence of the quartet critical current is « inverted », i.e., 𝐼 .% (𝛷 = 0) < 𝐼 .% (𝛷 = 𝛷 & /2) , suggesting an unusual quartet behavior occurs as we approach the high bias limit. Furthermore, for a fixed 𝛷, 𝐺 " (𝑉 . ) displays distinct non-monotonic behavior as 𝑉 . varies near 𝑉 +7 . As shown in Fig. 4c (the zoom-in 3D map) and Fig. 4d (line-cuts for flux in the range [-2.5𝛷 & , 0]), 𝐺 " (𝑉 . ) first decreases to yield a local minimum at 𝑉 . ≈ 𝑉 * (represented by the red sphere) and then increases for 𝑉 . > 𝑉 * . We note that 𝑉 * shifts in a zig-zag pattern in the (𝑉 . , 𝛷)-plane centered at 𝑉 +7 . Particularly, 𝑉 * (𝛷) is the largest at integer 𝛷 & and the smallest at halfinteger 𝛷 & , similar to the inverted quartet current in previous discussion. The non-monotonic variation of 𝐼 .% ?𝑉 . A and the inversion of the quartet current flux dependence provide a clue to the dynamic behavior of quartets in the non-equilibrium condition at a finite 𝑉 . . To understand the 𝑉 . dependence of quartet current, we need to consider the superconducting phase modulation due to the AC Josephson effect at finite bias. We first set the phase of the grounded loop 𝑆 & to be zero and the other two superconducting leads 𝑆 " and 𝑆 ! have phases 𝜑 " and 𝜑 ! , respectively. When voltages are applied to 𝑆 " and 𝑆 ! , the phases acquire time (t)-dependence following the Josephson 𝑡, we obtain a stationary quartet phase 𝜑 . and a running phase 𝜑 = that is periodically driving the system with a frequency 4𝑒𝑉 . /ℎ. In the adiabatic limit, i.e., 𝑉 . is much smaller than the Andreev minigaps 𝛥 & between the ABS pairs, one can take a time average of the ABS spectrum over 𝜑 = and obtain an effective ABS energy < 𝐸 >?@ >, which now only depends on the quartet phase 𝜑 . (see Section 5 in SI). For simplicity, we consider only a single pair of ABSs at a small bias, where the adiabatic approximation works. 𝐼 . , the supercurrent carried by quartets, can then be derived from the usual JJ currentphase relation: 𝐼 . = !: ℏ 𝜕 < 𝐸 >?@ >/𝜕𝜑 . . However, as 𝑉 . increases, we eventually enter the non-adiabatic regime, where occupation of higher ABSs must be accounted for. In this regime, the AC Josephson effect creates resonant coupling between the two adiabatic ABS levels (Fig. 4e). As a result, the effective separation of the two ABSs can be adjusted by the bias voltage in analogy to the Floquet bands 27,28 separated by 2𝑒𝑉 . , emerging from the periodically driven Bloch bands [START_REF] Mélin | Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction[END_REF][START_REF] Mélin | Engineering the Floquet spectrum of superconducting multiterminal quantum dots[END_REF] .

Employing the Floquet energy levels 𝐸 'BC.D:E that are derived from a pair of < 𝐸 >?@ > biased by the quartet bias 𝑉 . (Fig. 4e), we can now explain the experimentally observed non-monotonic behavior of 𝐼 .% (𝑉 . ). Figure 4f shows the evolution of two first-order 𝐸 'BC.D:E as a function of quartet phase 𝜑 . . The corresponding quartet current 𝐼 . (𝜑 . ), shown in the bottom panels, is obtained with the Floquet-Landau-Zener 30 consideration (see Section 5 in SI) and the critical quartet current 𝐼 .% (= 𝑚𝑎𝑥N𝐼 . ?𝜑 . AO) takes place at 𝜑 . * . As 𝑉 . increases, four different regimes appear: (I) for 2𝑒𝑉 . < 𝛥 & , no resonant coupling exists between the two < 𝐸 >?@ > and the quartet current is the same as near equilibrium. (II) 2𝑒𝑉 . ∼ 𝛥 & , i.e., the Landau-Zener (LZ) transitions between the two < 𝐸 >?@ > bands become appreciable, opening gaps between different 𝐹𝑙𝑜𝑞𝑢𝑒𝑡 bands. Hybridization between two levels and mixing of states that carry opposite directions of currents reduce the net quartet current, resulting in a drop in 𝐼 .% = 𝑚𝑎𝑥N𝐼 . ?𝜑 . AO) and the shifting of 𝜑 .

* . (III) At even larger quartet voltage 𝑉 . = 𝑉 * , the resonances occur at the 𝜑 .

* in (I), denting the peak in 𝐼 . and thereby 𝐼 .% reaches a minimum value. (IV) When 2𝑒𝑉 . is increased to be greater than the largest gap between the two levels, there is no more hybridization. Both the energy levels and the quartet current resume the nearly adiabatic situation, similar to (I). For a more accurate consideration, the non-equilibrium Keldysh formalism is applied to multi-level ABSs. It reveals that the inversion of 𝐼 .% (𝛷) can be associated with the avoided crossings due to LZ transition in the Floquet bands (see Section 5 of SI).

Methods

The van der Waals heterostructuremonolayer graphene on top of 40-60 nm thick hBNis assembled via the inverted stacking technique, where hBN serves as the dielectric substrate to minimize disorder [START_REF] Dean | Boron nitride substrates for high-quality graphene electronics[END_REF] . The flakes are picked up through procedure similar to the dry transfer technique 32 except the order is reversed, where the bottom hBN is picked up first. Via this method the top surface of graphene is guaranteed to be clean without any polymer contact in the assemble process. The superconducting contacts are made of 80 nm thick aluminum with 5 nm thick sticking layer of titanium, directly deposited on graphene through electron-beam evaporation at a pressure of low 10 FG torr. Each channel is designed to be 80-90 nm to ensure the existence of supercurrents among all of the superconductors. The measurements are performed in He-3 fridge with the base temperature 300 mK, well below the superconducting critical temperature of aluminum (Tc ~ 1.1 K) and the dual voltage source measurement scheme allows the detection of quartet signal (see Supplementary Information for the details).

S1. Dual voltage source for quartet measurement

In order to control the potential of each superconducting terminal, the quartets are detected through the dual voltage source measurement scheme (Fig. S1). Terminal 𝑆 ! and 𝑆 " are biased with DC voltages 𝑉 #! and 𝑉 #" through a voltage divider and an RC filter (in the main text the voltage dividers are not shown). The loop terminal 𝑆 $ remains grounded at all times but on top of this DC ground, we apply a small AC excitation in the range of 0.25-0.3 V. Like the other leads, this lead also has a voltage divider followed by an RC filter. The voltage divider for the loop S0 divides the AC excitation by 10 % . In order to detect the quartet current, we measure the conductance at the

S2. Comparison of currents at S1 and S2

Figure S2 shows the conductance 𝐺 & = 𝑑𝐼 & /𝑑𝑉 measured at terminals 𝑆 ! and 𝑆 " , respectively. Similar features can be found in both, including the Josephson currents between any two leads and the quartet current along 𝑉 ! = -𝑉 " . Overall the conductance at 𝑆 " is lower than that at 𝑆 ! , suggesting the asymmetric couplings between each pair of contacts.

S3. Quartet on top of the background quasiparticle signal

The quartet signal is much weaker compared to the Josephson signal. Besides the fact that quartet is an 8 th -order process as opposed to the 4 th -order of a Josephson current, the quartets exist outside of the zero-bias-voltage region, where signals from multiple Andreev reflections (MAR) are in the background. Figure S3a shows the color plot of the conductance 𝐺 " = 𝑑𝐼 " /𝑑𝑉 as a function of the bias 𝑉 ! and magnetic field while 𝑉 " is fixed at 6 V. Figure S3b shows the zoom-in scan around the quartet signal. The oscillations in magnetic field show a 3% variation of the total conductance (Fig. S3c).

S4. Gate dependence of the multi-terminal graphene Josephson junction

By applying a gate voltage, we can tune the chemical potential of the graphene channel region.

Moreover, the gate voltage can change the density of states of the graphene underneath Al contacts, modulating the couplings between the graphene and the superconductors.

S5. Theoretical complement for the interpretation of the experiment

This work focuses on the conductance modulation along the quartet line, 𝑉 ! = -𝑉 " = 𝑉, due to an applied flux. Along this line, where the microscopic models are solved, the quartet phase 𝜑 ' is stationary while the other conjugated phase variable 𝜑 * is time dependent. For a general JJ at a finite temperature, zero-bias conductance increases monotonically as the critical current increases [1]. In our multi-terminal JJ, a similar scenario occurs along the quartet line, where the amplitude of the quartet conductance 𝐺 ! (𝑉, -𝑉) increases monotonically as the critical quartet current 𝐼 '( (𝑉, 𝛷) increases [2]. Experimentally this is shown in Fig. S5. Therefore, the modulation of 𝐺 ! and 𝐺 " as a function of the applied flux and on the applied quartet bias reflect the modulation of 𝐼 '( (𝑉, 𝛷). Models present in reference [3-5] provide the « quartet current »-« quartet phase » characteristics 𝐼 ' (𝜑 ' , 𝑉, 𝛷) and one takes 𝐼 '( (𝑉, 𝛷) = 𝑀𝑎𝑥[𝐼 ' (𝜑 ' , 𝑉, 𝛷] on 𝜑 ' .

A. Flux periodicity of the conductance

The present device contains a loop in the « quartet source terminal » 𝑆 $ . The resulting interferences demonstrate the phase coherence of the DC quartet mode, despite the presence of biases.

Moreover, they exhibit oscillations with period 𝛷 $ /2 = ℎ𝑐/4𝑒 instead of 𝛷 $ .This is deeply different from a fundamental 𝛷 $ and a first harmonic 𝛷 $ 2 ⁄ , that would happen for a transparent SQUID made of two ordinary two-terminal junctions: here, (i) the loop only encloses only one junction, (ii) the quartet current flows from both branches 𝑆 $+ , 𝑆 $# towards contacts 𝑆 ! , 𝑆 " and (iii) the voltage bias prohibits DC Cooper pair current. So the correct interpretation of those two periodicities is instead: the 𝛷 $ 2 ⁄ period is the fundamental one, it signals the interference of quartets, revealing their charge 4𝑒. And the 𝛷 $ period is a subharmonic due to the possibility of splitting the quartets. The flux indeed directly affects the quartet process and can be used as a probe of the nontrivial effect of the voltage. This is essential for the interpretation of the non-monotonous

B=0 V qc (mV) G 1 (S)
𝐺(𝑉) variation found in Fig. 4 (main text). Note that the « inversion » found in 𝐼 ( (𝛷) as 𝑉 increases, namely 𝐼 '( (𝛷 = 0) < 𝐼 '( (𝛷 = 𝛷 $ /2) is counterintuitive: one would naively expect that destructive interferences in the 𝑆 $ loop decrease the quartet channel. The meaning of such an inversion is revealed by the perturbative diagrams shown on Fig.

S6

. The number of lines representing propagating amplitudes is limited by the transparency of the Graphene-Aluminum interfaces. First, the quartet « source » which is the grounded terminal can be either 𝑆 $+ or 𝑆 $# . In this case, both pairs forming the quartet emerge from the same branch 𝑆 $+ or 𝑆 $# , which we denote as Q processes. Alternatively, one pair can emerge from 𝑆 $+ and one from 𝑆 $# . The diagram in the center of Figure S6-1 corresponds to « splitting » the quartet in two entangled processes due to the exchange of two fermions [5]. We call this diagram FSQ (Fluctuating Split Quartet) because in a multichannel junction, due to spatial phase fluctuations, the dominant split quartet diagram that survives disorder has two more propagating lines (SQ) and involves the exchange of a quasiparticle between terminals 𝑆 $+ , 𝑆 $# .

The two Q-processes differ by the phase acquired by four electrons instead of two for an usual superconducting loop, yielding a periodicity 𝛷 $ /2 = ℎ𝑐/4𝑒 , whatever the interface transparencies at the contacts. In terms of phase, going from Q diagrams to SQ (FSQ) diagrams formally transfers one pair of the quartet 𝑆 $+ (resp. 𝑆 $# ) to 𝑆 $# (resp. 𝑆 $+ ), which implies a phase change 2𝜋𝛷/𝛷 $ . Therefore, the interference between processes Q and processes SQ (FSQ) creates a periodicity 𝛷 $ that reminds the one of an ordinary SQUID.

Explicating the quartet phase, one can write the sum of processes Q, SQ (or FSQ) as: with 𝑏 = 𝑑 ↓ 𝑑 ↑ and 𝛤(𝑡) = 𝛤 $+ 𝑒 &>/" + 𝛤 $# 𝑒 8&>/" + 𝛤 ! 𝑒 &[/ " @/ # (3)]/" + 𝛤 " 𝑒 &[/ " 8/ # (3)]/"

with 𝛤 & ∼ 𝜋𝑡 & " 𝑁(0) where 𝑁(0) is the Aluminum density of states. The reduced Hamiltonian 𝐻 123,< (𝑡) describes a driven two-level system and it can be solved with Floquet techniques. In fact the Hamiltonians 𝐻 123 (𝑡) and 𝐻 123,< (𝑡) describe a system periodically driven by the running phase 𝜙 * (𝑡) = 2𝑒𝑉𝑡/ℏ. This can be compared to the driving of a Josephson junction by a microwave field, with an important difference: here the drive amplitude is given by 𝛤 ! , 𝛤 " and is non-perturbative. Yet, there are similarities: an adiabatic regime holds when the drive frequency is much smaller than the equilibrium Andreev gap. And when it is comparable, Landau-Zener-like transitions occur that couple non-perturbatively the two Andreev levels [6].

Let us comment on the effect of the flux in the large gap limit. 𝛤(𝑡) can be rewritten as

𝛤(𝑡) = 𝛤 $ (𝛷)𝑒 &B(>) + 𝛤 ! 𝑒 &[C " @C # (3)]/" + 𝛤 " 𝑒 &[C " 8C # (3)]/"
with 𝛤 $ (𝛷) = a𝛤 $+ " + 𝛤 $# " + 2𝛤 $+ 𝛤 $# 𝑐𝑜𝑠𝛷, 𝑡𝑎𝑛𝛼(𝛷) =

D $% 8D $& D $% @D $& 𝑡𝑎𝑛𝛷/2
Therefore, in this limit the role of the loop is to map the four-terminal junction onto a three-terminal one with a flux-dependent coupling to Sc, together with a phase shift 𝛼(𝛷) that can be absorbed in the definition of the quartet phase 𝜑 ' . Nevertheless, the dependence of the quartet dynamics on the coupling 𝛤 ( is far from trivial, it is non-monotonous and thus the flux knob reveals the nonadiabatic effects that explain the experimental observation.

b. The adiabatic solution.

At a given time t, the instantaneous Andreev Bound State (ABS) energies are given by 𝐸 EF. (𝑡) = ±a𝜖 $ " + |𝛤(𝑡)| " . In the limit 𝑒𝑉 ≪ (𝜖 $ , 𝛤 & ) ≪ 𝛥, one can average out the slow drift motion of the phase. 𝜑 * (𝑡) i.e. on the period 𝑇 = ℎ/2𝑒𝑉 to yield adiabatic ABS, that only depend on the quartet phase 𝜑 ' and on the flux 𝛷.

⟨𝐸 EF. ⟩(𝜑 ' , 𝛷) = ± ! G ∫ $ G a𝜖 $ " + |𝛤(𝑡)| " 𝑑𝑡
Importantly, these effective adiabatic ABS do not depend on the voltage 𝑉. They give rise to an adiabatic quartet current 𝐼 ',+1&+# = (2𝑒/ℏ)𝜕⟨𝐸 EF. ⟩/𝜕𝜑 ' .

In the related case of a microwave-irradiated junction with frequency 𝜔, the adiabatic approximation is controlled both by the smallness of the parameter ℏ𝜔/𝛿 EF. (where 𝛿 EF. is the ABS mini gap at equilibrium) and by the small amplitude of the microwave field. Remind that in our case, even if 𝛿 EF. is not zero and 𝑒𝑉/𝛿 EF. is small, the periodic drive is strong.

d. Numerical solution of the dot model.

As 𝑉 increases in the experiment, the conductance oscillation has main period 𝛷 $ , then its frequency doubles with period 𝛷 $ 2 ⁄ , and at higher 𝑉 it recovers the period 𝛷 $ but with a phase shift equal to 𝜋. The frequency doubling corresponds to vanishing of SQ (FSQ) processes, leaving nearly pure quartet Qa, Qb processes interfering. Therefore, at a crossover voltage there is a change of the relative signs of the Q and SQ (FSQ) components.

This scenario is supported by numerical results obtained at nonzero voltage with the dot model and a finite superconducting gap. We use Keldysh non-equilibrium Green's functions to solve the dynamics of the model described by Hamiltonian 𝐻 123 (𝑡) [3]. The quartet current-phase characteristics is obtained for any 𝑉 and 𝛷. Typical parameters are 𝜖 $ = 0 (resonant dot) and:

𝛤 ! = 0.4𝛥, 𝛤 " = 0.2𝛥, 𝛤 $+ = (0.3𝛥 + 𝛾)/2, 𝛤 $# = (0.9𝛥 + 𝛾)/2
where 𝛾 controls the relative strength of the 𝑆 $ coupling relatively to the 𝑆 ! , 𝑆 " couplings. More generally, to obtain a 𝜋 -shift of the 𝐼 '( (𝛷) oscillation one needs: (i) a minimum asymmetry

|D $% 8D $& | D $% @D $&
of the contacts 𝑆 $+ , 𝑆 $# , (ii) a minimum ratio

D $% @D $& D ' @D ( , (
iii) small enough 𝜖 $ .

Figure S7 shows the quartet critical current as a function of 𝑉, for both 𝛷 = 0 and 𝛷 = 𝛷 $ /2 (with 𝛾 = 0.3). It contains two inversion regions, the main one being at higher voltage. Other narrower inversions are also observed at lower voltages (not represented here). Let us comment on the validity of the single level dot model. A numerical study of a manylevel dot model was also carried out, in a wide range of parameters so as to mimic a multichannel junction. Generically, regions of inversion are also found as the voltage is varied, showing the robustness of the phenomenon. Finally, preliminary calculations indicate that in a more general picture of a metallic junction, a more general reasoning based on Keldysh Green's function also gives rise to inversions. More theory is found in forthcoming papers [5].

Figure 1 .

 1 Figure 1. Single source voltage bias characterization of four-terminal Josephson junction including a loop. a, False color scanning electron microscopy (SEM) image of the device with measurement configurations. Graphene (purple) is top-contacted by Ti/Al superconducting electrodes (blue) and the electrode separations typically are 80-100 nm. b, 𝑉 -𝐼 curve of the device from the measurement configuration in a. 𝐼 ! is the critical current and the corresponding voltage value is labelled as 𝑉 ! (the blue dots). c, Magnetic field dependence, 𝑑𝐼/𝑑𝑉 as a function of the bias voltage and magnetic field. Bright orange region (high conductance) is the supercurrent and the edge corresponds to the value of critical current, which is modulated by the magnetic field. The SQUIDlike pattern indicates the interference between two supercurrent paths (red and blue dashed lines in a). The periodicity of the fast oscillation (white dashed curve) corresponds to the loop area and the slow oscillation (blacked dashed curve) is the first lobe of Fraunhofer pattern. d, Gate dependence of the supercurrent, 𝑑𝐼/𝑑𝑉 as a function of the bias voltage and global back-gate voltage 𝑉 "# . The critical current reaches the minimum as graphene is tuned to the Dirac point near 𝑉 "# = -32 V.

Figure 2 .

 2 Figure 2. Dual source voltage bias characterization for quartet detection. a, Configuration for the quartet measurement. The loop 𝑆 $ is grounded while potential of the first (𝑆 % ) and second ( 𝑆 & ) electrodes are controlled via DC voltages 𝑉 % and 𝑉 & , respectively. An additional AC excitation 𝛿𝑉is applied to the loop, and the AC currents 𝛿𝐼 % ( 𝛿𝐼 & ) through 𝑆 % ( 𝑆 & ) is measured. b, top panel: differential conductance 𝐺 % (= 𝛿𝐼 % /𝛿𝑉) measured at 𝑆 % as a function of the DC bias voltage 𝑉 % when 𝑉 & is tuned from 0.42 mV to 0.72 mV. Bottom panel: color plot of 𝐺 % as a function of 𝑉 % and 𝑉 & . In total, there are four different supercurrents in the device. Inset (i)-(iii) shows the local Josephson supercurrent between any pair of leads at the same potential. Inset (iv) Quartet shows the nonlocal quartet supercurrent flowing among all three superconducting leads and the quartet signal in (𝑉 % , 𝑉 & )-plane is the narrow yellow region along the -45 degree direction (where the red arrow points at). c, Schematic illustration of the three-terminal quartet process with the Andreev reflection picture. The middle superconductor 𝑆 $ is grounded while the other two superconductors are biased at +𝑉, -𝑉, respectively. The two entangled Cooper pairs (with red and blue electrons) are formed in 𝑆 $ through two local Andreev reflections and two cross Andreev reflections.

Figure 3 .

 3 Figure 3. Different types of quartet process. a, Left panel shows the quartet differential conductance 𝐺 & (= 𝛿𝐼 & /𝛿𝑉) measured at 𝑆 & a function of the flux 𝛷 = 𝐵 • 𝐴/𝛷 $ for 𝑉 "# = 25 V. Satisfying the quartet bias condition, 𝑉 % = -𝑉 & is fixed at 4 V. Right panel shows the analysis from fast Fourier transform (FFT) with a prominent second harmonic. b, for 𝑉 "# = 26-30 V. The periodicity evolves from half-flux quantum to one flux quantum as 𝑉 "# increases. c, Subfigure (Qa)(Qb) shows the conventional three-terminal quartet process with only one out of the two loop contacts involved. Electron-hole conversion happens twice at the same contact of the loop (either 𝑆 $' or 𝑆 $" ), resulting in periodicity of half-flux quantum. Subfigure (SQab) shows the split-quartet process involving both contacts of the loop. With the odd parity of Cooper pairs transferred, the periodicity is one flux quantum.

  Fig 2c describes the formation of CQ-ABS: two Cooper pairs from two Scontacts (𝑆 " and 𝑆 ! ) are entangled into a four-electron state via two local Andreev reflections and two cross Andreev reflections at the middle S-contact (𝑆 & ) 7-11 . Remarkably, at the high bias regime where the local DC-Josephson currents disappear, the quartet ABSs persist when the junction is biased anti-symmetrically and carry nonlocal supercurrent flowing among all terminals simultaneously. The corresponding bias condition 𝑉 " + 𝑉 ! = 0 satisfies the energy conservation for the CQ-ABS, where correlated Cooper pairs originating from 𝑆 " and 𝑆 ! are transmitted into 𝑆 & .

Figure 4 .

 4 Figure 4. Quartet conductance and the Floquet spectrum as a function of Vq and magnetic flux. a, Quartet conductance 𝐺 % measured along the quartet line in (𝑉 ( , 𝛷)-plane. The red dashed line traces the minimum conductance for -2.5 < -𝛷/𝛷 $ < 0 and the red sphere represents the local minimum at 𝛷/𝛷 $ = -2. b, waterfall plot of 𝐺 % (𝛷) for 𝑉 ( = 6.9-7.6 𝜇V. It shows clear evolution of 𝐺 % from maxima to minima at inter values of flux. At the critical quartet 𝑉 ( ≈ 𝑉 )* ≡ 7.2 𝜇V, periodicity is 𝛷 $ /2 and for 𝑉 ( > 𝑉 )* , the quartet critical current is « inverted ». c, Zoom-in surface plot of 𝐺 % (𝑉 ( , 𝛷) for -2.5 < 𝛷/𝛷 $ < 0. The winding of the red sphere (local minimum) is marked with the red dashed line, matching that in Fig 4a. The gray spheres represent quartet conductance at different values of 𝑉 ( . d, waterfall plot of 𝐺 % (𝑉 ( ) for 𝛷/𝛷 $ = -2~ 0. The local minimum 𝑉 * presents a zig-zag pattern as flux is tuned. e, When the quartet voltage 𝑉 ( is in the adiabatic limit, the effective Andreev levels < 𝐸 ,-. > depend only on one phase variable, the quartet phase 𝜑 ( . The minimum difference between the two levels is the Andreev gap 𝛥 $ and a finite 𝑉 ( creates resonant coupling between the two levels. f, upper panel shows the energy of the Floquet states as a function of the quartet phase 𝜑 ( at different values of 𝑉 ( . The corresponding quartet current 𝐼 ( carried by these Floquet states is shown in the lower panel. The gray and red spheres mark the critical values of the quartet current 𝐼 (! = 𝐼 ( (𝜑 ( * ), matching the ones in Fig. 4c. In (III), the red sphere denotes 𝑉 ( =𝑉 * when 𝐼 (! reaches a local minimum, reflecting an avoided crossing in the Floquet spectrum.

  relation 12 : 𝜑 • " (𝑡) = !:; ! < , 𝜑 • ! (𝑡) = !:; " < . Under the quartet condition (𝑉 " = -𝑉 ! ) and by choosing a new set of phase variables 𝜑 . ≡ 𝜑 " (𝑡) + 𝜑 ! (𝑡), 𝜑 = ≡ 𝜑 " (𝑡) -𝜑 ! (𝑡) = 3:; $ <

  biased terminals 𝑆 ! and 𝑆 " . As shown in the circuit, we use lock-in amplifier to measure the potential 𝑑𝑉 ! and 𝑑𝑉 " . The AC currents owing from are then given by 𝑑𝐼 & = 𝑑𝑉 & /𝑟, where 𝑖 = 1,2. Therefore, the conductance at each lead is 𝐺 & = 𝑑𝐼 & /𝑑𝑉 = 𝑑𝑉 & /(𝑟 • 𝑑𝑉).

Fig. S1 :

 S1 Fig. S1: Schematic diagram of the dual voltage source for quartet measurement.

Fig. S2 :

 S2 Fig. S2: Comparative data between 𝐺 ! = 𝑑𝐼 ! /𝑑𝑉 and 𝐺 " = 𝑑𝐼 " /𝑑𝑉 as a function of 𝑉 ! and 𝑉 " .

Fig. S3 :

 S3 Fig. S3: a. 𝐺 " = 𝑑𝐼 " 𝑑𝑉 ⁄ as a function of the DC bias voltage 𝑉 ! and magnetic field when 𝑉 " is fixed at 0.6 V. The field-dependent quartet supercurrent is in the white box and the zoom-in scan is shown in b. Panel c shows the quartet signal on top of the quasiparticle background (blue dashed line). 𝑉 '( is the voltage corresponding to the quartet critical current 𝐼 '( .

  Fig.S4: 𝐺 ! (𝑉 ! , 𝑉 " ) at 𝑉 #) = -10 V, -5 V, and 40 V. Among these back-gate voltages, the quartet supercurrent (along 𝑉 ! = -𝑉 " ) is the strongest at 𝑉 #) = -5 V.

Fig. S5 .

 S5 Fig.S5. Experimentally, the quartet conductance 𝐺 ! along the 𝑉 ! = -𝑉 " = 𝑉 indeed is found to increase monotonically as 𝑉 '( increases at a fixed bias voltage with varying magnetic flux (left panel). Same monotonic relation between the quartet conductance and quartet critical current for a fixed magnetic field with varying bias voltage 𝑉 is shown in the right panel.

Fig. S6 .

 S6 Fig.S6. Representation of the lowest order quartet processes. (Left) Q-processes. (Middle) FSQprocess, a split quartet process that vanishes by statistical fluctuations in a multichannel diffusive junction. (Right) SQ-processes.

  𝐼(𝜑 ' , 𝛷) = 𝐼 (,-+ 𝑠𝑖𝑛(𝜑 ' -𝛷) + 𝐼 (,-# 𝑠𝑖𝑛(𝜑 ' + 𝛷) + 𝐼 .-𝑠𝑖𝑛 𝜑 ' Here the prefactors can take positive or negative values. Quartets are generically π-junctions in the tunnel regime and at vanishing voltage, i.e., 𝐼 (,-& < 0, (i=a, b). Taking the maximum with respect to 𝜑 ' of 𝐼(𝜙 ' , 𝛷) gives the critical current. For 𝛷 = 0 one has 𝐼 '( (0) = |𝐼 (,-+ + 𝐼 (,-# + 𝐼 .-| while for 𝛷 = 𝛷 $ /2 one has 𝐼 '( (𝛷 $ /2) = |𝐼 (,-+ + 𝐼 (,-# -𝐼 .-|. The relative sign of 𝐼 (,-+,# and 𝐼 .- thus governs the flux variation of 𝐼 '( . If it is positive, the total quartet critical current has a maximum at 𝛷 = 0 and a minimum at 𝛷 = 𝛷 $ /2 , ie 𝐼 '( (𝛷 = 0) > 𝐼 '( (𝛷 = 𝛷 $ /2) . If it is negative, the minima and maxima are inverted and 𝐼 '( (𝛷 = 0) < 𝐼 '( (𝛷 = 𝛷 $ /2). Importantly, a pure 𝛷 $ 2 ⁄ periodicity implies that the SQ channel is absent, leaving only the Q contributions. In a perturbative limit, no inversion is found. The next section explains how the new control variable 𝑉 can indeed trigger an inversion of the sign of 𝐼 '( (𝛷 = 0) -𝐼 '( (𝛷 = 𝛷 $ /2). B. The dot model, numerical results and the Floquet-Landau-Zener interpretation a. The dot model. The dot model [3] treats the metallic junction as a 0D object with a single level having one-electron energy 𝜖 $ 2 ⁄ , no Coulomb interaction and coupled to the four terminals by one-electron matrix elements 𝑡 & 𝑒 &/ ! /" . Here i=(1, 2, 0a, 0b) and the superconducting phases are incorporated in the matrix elements. With a convenient gauge choice, the phases 𝜑 & are 𝜑 ! = [𝜑 ' + 𝜑 * (𝑡)]/2, 𝜑 " = [𝜑 ' -𝜑 * (𝑡)]/2, 𝜑 $+ = 𝛷/2, 𝜑 $# = -𝛷/2 with 𝜑 * (𝑡) = 2𝑒𝑉𝑡/ℏ.

Figure

  Figure S7. (Left) Maximum quartet current for 𝛷 = 0 (black) and 𝛷 = 𝛷 $ /2 (red), showing two « inversion » windows. (Right, bottom) Same but on an extended voltage range. (Right, top) The corresponding Andreev-Floquet ladders, showing the correlation of the anticrossings with the minima of 𝐼 '( .

Figure

  Figure S7 also shows a part of the Floquet spectrum (inside the superconducting gap) as a function of the reduced voltage 𝑒𝑉/𝛥, in a more extended voltage range. The plot represents 𝐸 I,± /𝑒𝑉. The anticrossings are visible around precise voltage values, and they get more and more frequent at low voltage. The quartet critical current 𝐼 '( is represented for both 𝛷 = 0 and 𝛷 = 𝛷 $ /2. The minima of 𝐼 '( are perfectly correlated to the resonances. Like for a microwaveirradiated junction, the anticrossings manifest a quantum mixing of the adiabatic states (𝑛+, 𝑚-), that bear opposite indices therefore carry opposite currents. As a consequence, in the region of the anticrossing, quantum fluctuations reduce the quartet current 𝐼 '( .

Figure

  Figure S8. (Right) Evolution of the quartet current-phase characteristics through a Landau-Zener resonance (from a2 to d2). (Left) The corresponding evolution of the Andreev-Floquet bands.

  The dot energy 𝜖 $ mimics the control of the metallic junction by a gate. This model can be generalized to several noninteracting levels with energies 𝜖 & .The model can be further simplified in the large gap limit 𝛥 ≫ 𝜖 $ , 𝑡 & . Single particle processes are eliminated out and only pair processes remain: 𝐻 123,< (𝑡) = 𝜖 $ (2𝑏 6 𝑏 -1) + 𝛤(𝑡)𝑏 + 𝛤 * (𝑡)𝑏6

	𝐻 123 (𝑡) = ∑ &45	𝜖 &45 𝑐 &45 6 𝑐 &45 + ∑ &4 𝛥(𝑐 &4↑ 6 𝑐 &,84↓ 6	+ 𝐻. 𝑐. ) + ∑ &45	[𝑡 & 𝑒 &/ ! (3)/" 𝑐 &45 6 𝑑 &5 + 𝐻. 𝑐. ]
		+ 𝜖 $ ∑ 5	𝑑 5 6 𝑑 5
	The Hamiltonian writes:

Acknowledgements We thank B. Douçot for his collaboration on the Floquet theory. K.-F.H. acknowledges support from DOE (DE-SC0019300) for sample preparation and fabrication. Y.R. acknowledges support from NSF (QII-TAQS MPS 1936263) for device characterization. P.K. acknowledges NSF (DMR1809188) for data analysis. R.M acknowledges the use of the resources of the Mésocentre de Calcul Intensif de l'Université Grenoble-Alpes (CIMENT). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001, JSPS KAKENHI Grant Number JP20H00354 and the CREST(JPMJCR15F3), JST.

Author contributions Y.R., K.-F.H. and P.K. designed the experiment. P.K. supervised the project. K.-F.H. and Y.R. fabricated the devices. T.T and K.W. provided single crystals of hBN. K.-F.H. and Y.R. performed the measurements. K.-F.H., Y.R., and P.K. analyzed the data. R.M. and D.F. carried out the theoretical modelling. K.-F.H., Y.R., and P.K. prepared the manuscript and Supplementary Information with input from all the authors.

SUPPLEMENTARY INFORMATION

Interference of Cooper quartet Andreev bound states in a multi-terminal graphene-based

Josephson junction

Ko-Fan Huang 1 † , Yuval Ronen 1 † , Régis Mélin 2 , Denis Feinberg 2 , Kenji Watanabe 3 , Takashi Taniguchi 4 , Philip Kim 1,5 *


O A Otmakhova

A A Piryazev

G N Bondarenko

G A Shandryuk

A V Maryasevskaya

A S Merekalov

D A Ivanov

R V Talroze

New complexes of liquid crystal discotic triphenylenes: induction of the double gyroid phase

Electron donor-acceptor liquid crystals have been attracting considerable attention due to possible applications in optoelectronics and photonics. The creation of such charge transfer complexes is a powerful and flexible instrument for modifying the structures and properties compared to those of the initial components. In the present work, such an approach is exemplified on new complexes formed via non-covalent interactions of triphenylene discotics, namely, 2,3,6,7,10,11hexakis(pentyloxy) triphenylene (H5T) and 2-(acryloyloxypropyloxy)-3,6,7,10,11-pentapentyloxtriphenylene (TPh-3A), with an electron acceptor, β-(2,4,7-trinitro-9fluorenylideneaminooxy) propionic acid (TNF-carb). The structure of thin supported films of H5T, TPh-3A and their blends with TNF-carb was investigated by grazing-incidence wide-angle X-ray scattering using a synchrotron source. At room temperature, the pristine discotics crystallize in orthorhombic unit cells whereas the selfassembly of H5T and TPh-3A with TNF-carb results in a double gyroid and hexagonal phases, respectively. Formation of the double gyroid phase with the lattice parameter of 36.5 Å is driven by phase separation between the aromatic and alkyl regions of the system. It is supposed that the TNF-carb molecules of the complex are positioned in the nodes of the structure while the H5T molecules are located in the struts adjoining the nodes via triple junctions. For the hexagonal crystal of the TPh-3A /TNF-carb complex, the acceptor molecules are likely located in the intersticies between the neighboring supramolecular columns of TPh-3A. The molecular structures of the blends were also explored by means of FTIR spectroscopy. A detailed FTIR spectra analysis illustrates fine changes in intermolecular bonds. For example, the initially dimerized acceptor molecules totally disappear in the complex structures whereas in TPh-3A/TNF-carb additional H-bonds between the carboxylate group in TNF-carb and the ester group of TPh-3A form. The experimental data allows putting forward possible molecular models of the complex structures.

Introduction

Discotic liquid crystals (discotics) characterized by 1D photoconductivity are of special interest for photovoltaic and other electronic applications [1]. Such properties are caused by particular columnar packing of disc-like molecules, which are prone to π -π interactions between their aromatic cores [2]. In some instances, discotic molecules form thermotropic cubic bicontinous phases, which may act as alignment-free 3D πelectronic semiconductors [3]. To modify the conductivity of discotics one can add electron acceptors to form charge transfer (CT) complexes with electron-donor discotic molecules [4]. Wöhrle et al [5] discuss in detail the band-gap structure of the systems based on discotic liquid crystals as well as conditions influencing the mobility of charge carriers. The high mobility and relatively simple processing of discotic liquid crystals may help developing these systems as an alternative to conventional semiconductors. Kaafarani [1] specifically mentions possible applications of discotic liquid crystals for organic electronic devices. The priorities of selforganized columnar systems with the π-π stacking and donoracceptor complexes with 2,4,7-trinitro-9-fluorenone (TNF) are discussed as well. Bin Mu with coauthors [6] focus on columnar LC materials displaying both high electrical conductivity and strong luminescence for the cases when hydrogen bonds additionally stabilize CT complexes. TNF is known to have an almost planar conformation and to crystallize into a monoclinic structure [7]. It has exceptional spectroscopic and photochemical properties [8,9]. Haverkate et. al [10] used a discotic molecule, 2,3,6,7,10,11hexakis(hexyloxy)triphenylene (H6T), in a blend with TNF. By means of the NMR and Raman spectroscopy the authors found evidence for the ground-state electron transfer from H6T core to TNF although the estimated amount of charge involved is pretty low (0.06 electron). Different intermolecular electronic transitions comprise the excited CT-band of H6T/TNF complex. The lowest excited state is a π-π * type of transition from the HAT6 HOMO on the aromatic core to the LUMO of TNF. Thus, the control over electronic properties in such materials may be achieved via the complex formation as a powerful and versatile tool allowing tuning the energy levels of the donor and acceptor while changing the overall supramolecular structure. Previous reports allow comprehending the role of the chemical structure in the discotic/TNF complex formation and its packing in a LC phase. Indeed, in publications by the Ringsdorf's and Wendorf's groups the authors consider that the TNF acceptor molecule is incorporated into the columns formed by discotics being sandwiched between the donor molecules [11]. On the other hand, Kruglova et al. [12] and Haverkate et al. [13] put forward a structure with TNF molecules located outside the columns in the aliphatic tails regions. Moreover, in the framework of the model proposed in [13] the TNF molecules are aligned along the long columnar axes. Such a difference of the models of the systems even in the case of the same acceptor, i.e. the TNF molecule, complexed with very similar discotic liquid crystals such as H6T and 2,3,6,7,10,11hexakis(pentyloxy)-triphenylene (H5T) raises the issue about the role of different chemical structures and bonds between the components on the structure of the complex. The main goal of the current paper is to analyse the complex formation involving different symmetrical and nonsymmetrical electron-donor discotic molecules and a new electron acceptor. In the present work, we put the focus on the structure of the complexes and the constitutive complex components and on the analysis of the types of bonds responsible for the complex formation and stability. For the purpose of the study, we selected two triphenylene-containing molecules, namely, well-known H5T as a symmetrical molecule and an acrylic monomer 2-(acryloyloxypropyloxy)-3,6,7,10,11-pentapentyloxy-tripheny-lene (TPh-3A) as a nonsymmetrical one. The chemical structures of the molecules mentioned above are given in Figure 1. We have selected these molecules for the

OC5H11 C5H11O C5H11O OC5H11 OC5H11 OC5H11 OC5H11 H11C5O H11C5O OC5H11 OC5H11 O(CH2)5OOCCH CH2 H5T TPh-3A C N O(CH2)2 C O OH NO2 O2N NO2
TNF-carb present study assuming that the difference in their structure may affect the structure of the complex as a whole. The insertion of the functional groups in the discotic molecule may provide additional bonding between the complex components.

The systems under study are prepared by mixing discotic triphenylene-containing molecules having different substituents with the electron acceptor, β -(2,4,7-trinitro-9-fluorenylideneimino-oxy)propionic acid (TNF-carb). With the analysis of the structure and electronic characteristics obtained from the quantum chemical calculations given in [14] we have shown that a condensed aromatic system with three nitro groups can be a highly effective electron acceptor with a strong propensity to form intermolecular π-π stacking interactions. Moreover, these systems are capable of forming H-bonded cyclic dimers. TNF-carb may be bonded to four donor molecules such as H5T or TPh-3A due to π-π interactions and hydrogen bonding (H-bond). Therefore, we focus the present research on systems with stoichiometry 4:1, i.e. containing four discotic molecules per one TNF-carb. The interest in such systems is also related to the fact that the 2-(acryloyloxypropyloxy) group in the discotic molecule will allow further polymerizing the complex.

Results and discussion

Structure of the pristine discotics and their blends with TNF-carb

The DSC curves of H5T (a) and TPh-3A (b) are shown in Figure 2. Both curves exhibit two peaks on heating and cooling. The first melting peaks under heating at 65 for H5T and 55 oC for TPh-3A are characterized by relatively high enthalpies of 43.4 and 59.1 J/g, respectively, which serve as indications of the crystalline structures of the pristine discotics. The polarized optical microscopy (POM) data support the idea about the crystalline state of discotics at room temperature. As it is shown in Figure 3 the crystals of both discotic compounds have herring-like (a) and spherulitic optical textures (b). They melt with formation of focal conic and mosaic textures (Figure 3c,d) pertinent to liquid crystalline phases. The transitions to the isotropic phase occur at 117.5 and 93.4 oC for H5T and TPh-3A, respectively (Figure 2). The attempts to solve the crystal structure of hexakis (alkoxytriphenylens) were previously done by M. Cotrait et al. [15] but due to several reasons they remained unsuccessful. Subsequently, in the work by T. Wang and co-authors [16], the crystal structure of H5T was indexed to an orthorhombic cell with a P2212 space group having the following cell parameters: a=36.73 Å, b=27.99 Å and c=4.91 Å. According to the report, the molecules in the unit cell are organized in a herring-bone type arrangement where the aromatic cores of the molecules are inclined by 48o with respect to the ab-plane of the lattice. In the present work, we use a synchrotron source to explore the supramolecular structures of H5T, TPh-3A and their complexes with TNF-carb employing X-ray scattering in wide angles in grazing-incidence geometry (GIWAXS). As can be seen from Figure 4, the 2D X-ray patterns recorded on thin films of the studied compounds exhibit crystalline structures (Figure 4a,b). Indeed, the GIWAXS data shows crystalline reflections with mixed h, k and l Miller indices testifying that the samples form 3D crystals (Table 1). This conclusion from GIWAXS is confirmed by the thermal analysis and POM. Moreover, the diffractograms display pronounced textures. Thus, on the GIWAXS pattern of H5T, the hk0 diffraction peaks display preferential orientation on the meridian of the pattern, which corresponds to the planar orientation of the directspace c-vector of the lattice. Although the relative intensities of the peaks qualitatively match the ones reported in [17], their dspacings are slightly smaller than the ones in the cited report. In Table 1, we present the experimental d-spacings, as well as their fits to the different structural models. It can be seen that the adjustment of the peaks of H5T to an orthorhombic lattice provides a good match of the experimental and fitted values. The extracted lattice parameters are a=32.8 Å, b=26.5 Å, c=4.7 Å, which correspond to the density of the crystal phase of 1.21 g/ml for 4 molecules per unit cell. The extracted lattice parameters are somewhat smaller than the ones found in [16], which might be due to a different sample preparation method.

The studied film of TPh-3A also reveals an orthorhombic unit cell with the following parameters: a=34.1 Å, b= 27.3 Å, c=4.5 Å.

As compared to the unit cell of H5T, the relative increase in the lateral lattice parameters may reflect the additional space required to pack the modified side chain of TPh-3A containing a double bond. Interestingly, the film texture of TPh-3A is clearly different from that of H5T. First of all, it is much better oriented because it displays point-like reflexes instead of arcs of a circle. Secondly, the texture of the film is likely biaxial instead of a simple planar texture of H5T that might stem from crystallization of the parent high-temperature hexagonal columnar mesophase [18,19], with the columns being oriented in the plane of the film.

In the case of TPh-3A, the c parameter of the unit cell is also lying in the plane of the film. The sample probably exhibits large single-crystalline domains with a size comparable or larger than the X-ray beam crosssection. Blending of H5T and TPh-3A with TNF-carb dramatically modifies their structures. Indeed, the corresponding diffraction patterns (cf. panels c and d of Figure 4)

show the presence of a gyroid and hexagonal phases, respectively. The assignment of the observed gyroid phase to a double gyroid is based on the selection rules summarized in a recent work [19]. The double gyroid phase, which is a bicontinuous cubic phase, displays a typical orientation in thin films in which the intense 211 reflection is oriented along the meridian of the pattern [20]. The a-parameter of a cubic lattice of this double gyroid phase is 36.5 Å. The change of the high-temperature liquid-crystalline hexagonal columnar phase of pure H5T to a double gyroid structure upon complexation with TNF-carb is likely to be connected to modification of the curvature of the interphase between the aromatic and alkyl regions of the systems as discussed in [21,[START_REF] Gearba | Molecular vibrations: The theory of infrared and Raman vibrational spectra[END_REF]. The extent of the interphase curvature in this case is believed to be intermediate between that of a hexagonal columnar phase and a flat smectic phase. This change is clearly caused by modification of the geometry of the elementary building block, the molecular details of which will be analysed further with the use of FTIRspectroscopy.

As for the optical texture presented in Figure 3a, it is focal-conic and differs from the expected isotropic optical texture known for the gyroid phases. However, as it is seen in Figure 4c the diffraction pattern exhibits the characteristic intra-columnar peak typical of the ordered high-temperature hexagonal phase of H5T. We speculate that the system possibly contains remnants of the supramolecular columns, which might be indicative of a different stoichiometry of the blend in the double gyroid phase. For the case of the TPh-3A/TNF-carb complex, one observes a GIWAXS pattern that can be indexed to a hexagonal crystal with the following parameters: a=b=47.6 Å, c=3.5 Å, alpha=beta=90o, gamma=120o. The c-parameter is lying in the plane of the film, which makes the film texture similar to the one observed for Taking into account the complex formation between the two components it is important to understand what type of noncovalent bonds is responsible for the complex stability. To tackle this issue, we have carried out FTIR measurements described in the following section.

Molecular structure of the blends

The comparison of FTIR spectra of H5T, TPh-3A, TNF-carb and the blends of 4:1 compositions (Table 2) shows that the FTIR spectrum of the blends is not an additive composition of the spectra of both components (Figure S1). Many spectral bands change both the relative intensities and positions of maxima. It proves the fact that the blend is not a simple mechanical mixture but a complex in which components are interacting. The analysis of Table 2 data shows that the major changes in the blends spectra proceed in the absorption range of carboxyl group. The stretching band at 1703 см-1 related with С=О bond in carboxylic group of TNF-carb shifts down to 1710 cm-1 in the spectra of H5T/TNF-carb and TPh-3A/TNF-carb blends. On one hand, this shift towards shorter wavelengths serves as a sign of the increase in the electron density on that bond. On the other hand, 1703 cm-1 band (νC=O in C(O)OH) in TNF-carb spectrum is shifted in the longwave region because these bands in carbonic acids spectra are usually located above 1710 cm-1. Most likely, this means that the carboxylic groups in the solid TNF-carb form hydrogen bonds (H-bonds) as shown in Scheme 1.

Scheme 1. Association of carboxylic groups in TNF-carb molecules in a dimer.

In such a dimer the delocalization of electron density (not lower, than С2v). In accordance with the theory of oscillation spectra [23] in spectra of systems of high symmetry the frequency degeneracy is manifested. It corresponds to the appearance of frequencies with equal energy of oscillation and wavelength. The latter results in the decrease of the number of absorption bands. In the case of TNF-carb the associates of such a kind have three broad bands between 2800 and 2400 cm 1 (Figure 6a, Table 2). The bands are not present in the spectrum of H5T/TNF-carb (4:1) but one can see instead five new bands (Figure 6a). It serves as indication of the disappearance of the symmetrical dimer and proves the formation of new less symmetrical associate: Scheme 2 shows the possible structure based on carboxylic group of TNF and electronegative oxygen atom in the ether group of H5T.

Scheme 2. Association of the carboxylic group in TNF-carb with the ether group in H5T.

The local symmetry of such associate (Scheme 2) is much lower (Сs) than that in TNF-carb dimer (Scheme 1). It is accompanied by the removing frequency degeneracy manifested by the increase in the number of bands up to 5 in IR spectra of the blends (Figure 6b and Table 2). In addition the delocalization of the electron density in less symmetrical dimer (Scheme 2) is lower than that in the symmetrical one (Scheme 1) and νС=О band is shifted down to 1710 cm-1. At the same time absorption bands related with С-О-С bonds and angles in 1210-1160 cm-1 range are shifted in the spectrum of the blend in comparison with that of H5T and TPh-3A (Table 2).

As for systems, containing TPh-3A there is a difference in the spectral range of C=O stretching vibration. There are two bands at 1734 and 1710 сm-1, which do not coincide with similar bands in the initial components at 1703 сm-1 (TNF-carb) and 1724сm-1 (TPh-3A) (Table 2). It means that every band is shifted to a shorter wavelength. One also observes changes in the range of carboxylate associates (2500-2800 cm-1): the bands related with TNF-carb dimer disappear and five new though weak broad peaks appear (Figure 6b) that coincide with the bands of the similar blend H5T/TNF-carb. One can suppose that in that blend two types of interactions exist as well but in addition, the carboxylate group in TNF-carb forms a H-bond with the ester group of TPh-3A (Scheme 3).

Scheme 3. Association of carboxylic group of TNF-carb with the TPh-3A acrylate group.

Thus, one can state that hydrogen bonds are definitely responsible for the formation of blends. However, we also observe the strongest changes in the blends spectra in comparison with those of individual components in the range of nitro group absorption (1530 -1320 сm-1) as well as in the absorption wavelength range 910 -700 сm-1, which is related with out-of-plane oscillation deformation of CCH group in aromatic cores (Table 2). An additional stabilization of the blend components is possible due to donor-acceptor interaction between the electron deficient carbon atoms in aromatic core of TNF-carb located in orthoposition related to nitro groups and electron donor ether groups in H5T or TPh-3A. The interaction of such type has to induce slight changes of valence angles in both nitro groups and the neighbouring C-CH angles within TNF-carb structure and valence angles (Ph)CO-C(Alk) and alkyl ligand conformation in H5T or TPh-3A. The latter will lead to the shift of bands in the absorption range of nitro groups, out-of-plane deformation oscillations δCCH in TNFcarb aromatic cores as well as in the range of deformation oscillations of alkyl groups. It is well seen in the spectra of Н5Т/TNF-carb (or TPh-3A) (Table 2). Due to TNF-carb molecule contains three nitro groups providing donor-acceptor interactions and one carboxylic group participating in H-bond it is easy to imagine the optimal ratio of Н5Т/TNF-carb (or TPh-3A) to be 4:1.

If one compares the FTIR spectra of H5T/TNF-carb blends with different component ratios 1 -4:1, 2 -2:1 (Figure S2a) the absorption region of the bands from the carboxyl group and associates in these spectra looks exactly the same. The difference between the spectra of blends of different compositions lies in the fact that the intensities of the bands from nitro groups in the spectrum of the H5T/TNF-carb composition equal 2:1 decrease less noticeably in comparison with the spectrum of the 4:1 composition. In addition, two bands from nitro groups (1526 and 1344 cm-1) and from outof-plane С-СН vibrations of aromatic rings (850-700 cm-1) are more split than in the spectrum of 4:1 blend. In the case of TPh-3A/TNF-carb 4:1 blend the spectrum shows two bands of C=O groups at 1710 and 1734 cm-1 shifted to the shorter wavelengths than those of components (Table 2).

In the spectra of blends of different compositions (Figure 7) one can see one wide and splitted band in this range. It allows supposing, that blends may contain both associates and separate components creating the overlap of several bands in C=O absorption region. As for 2800-2400 сm-1 this spectral region for different compositions 3:2, 1:1 и 2:3 is not that informative due to very weak, non-resolved bands (Figure S2b). Thus, the analysis of FTIR spectra of Н5Т/TNF-carb and TPh-3A/TNF-carb blends of different compositions show that between components complexes may be formed when isolated from solutions. This can only be explained by the fact that complexation in mixtures of different compositions occurs with the participation of the same functional groups, but the complexes formed in the case of 2:1 composition are less symmetric (or more diverse) than those of 4:1 composition.

Models of the blend structures

The acquired X-ray data can help us proposing molecular models of the complexes. For the H5T/TNF-carb complex, one can readily estimate the number of molecules in the unit cell. Indeed, we recall that the unit cell of the double gyroid phase contains 16 nodes and 24 struts connecting them, whereby the structure is composed of triple junctions of the struts. Since the acceptor is capable of complexing several H5T molecules it seems reasonable to suppose that the nodes are occupied by TNFcarb. Each strut then can contain an integer number of H5T molecules, which probably equals one because of the calculated density values. The distance between the nodes is given by (a√2)/4=12.8 Å. This is compatible with the size of the aromatic core of H5T. Figure 8a shows schematics of the proposed molecular arrangement in the double gyroid phase overlaid on the conventional representation of the phase based on the known trigonometric equation (cf. e.g., [24]). The green channels in this representation correspond to the volume occupied by the aromatic molecular fragments while the rest of the unit cell is filled with the phase-segregated alkyl tails. The difference between the overall stoichiometry of the blend and that of the proposed structure can account for the birefringence of the observed optical texture, which is not isotropic as it should have been for a pure gyroid phase. We speculate that the excess of H5T can segregate out of the gyroid domains and self-assemble revealing the characteristic features of the columnar stacking typical of the bulk H5T in the corresponding diffraction pattern.

As far as the structure of the TPh-3A/TNF-carb complex is concerned, it can be thought of as a hexagonal system in which the acceptor molecules are located in the interstices between the columns as shown in Fig. 8b. One can conclude that even a small modification in the structure of H5T can result in a significant variation of the structure of its complex with TNF-carb. In particular, addition of a relatively small but asymmetric 2-(acryloyloxypropyloxy) group on one of the alkyl arms of H5T makes it changing the symmetry of the phase from cubic to hexagonal. Such impact of a small substituent on the final supramolecular structure can be accounted for by its H-bonding with the carboxylic group of TNF-carb.

Experimental

Synthetic procedures. I. Synthesis of 2,3,6,7,10,11hexakis(pentyloxy)triphenylene (H5T). H5T was synthesized according to the well-known process described elsewhere [25,26]. The synthesis was carried out according to the procedure described in [26]. 22 g of benzoate, 90.6 g of brompentane, 42.9 g of potassium carbonate and 110 ml were placed in a 500 ml round-bottom flask. ethanol. The resulting mixture was boiled for 18 hours in an inert atmosphere of argon. After that, 110 ml of methylene chloride was added to the reaction flask, the solution was separated from the precipitate, and the precipitate was washed three times with methylene chloride. The washing solutions were combined with the basic solution and evaporated. The result was a dark brown oil weighing 30 g. The product was distilled in vacuum. The boiling point of the product is 101-108 °C (at 0.9 * 10-3 atm). Yield 85%.The main paragraph text follows directly on here.

II
2. Synthesis of 2-hydroxy-3,6,7,10,11-pentapentyloxytriphenylene.

22 g of benzoate were placed in a 250 ml round bottom flask, 50 ml of dry methylene chloride were added, and the reaction flask was filled with argon while stirring. Then, 13 g of iron trichloride and 5 drops of concentrated sulfuric acid were added to the reaction flask in three sets at intervals of 15 minutes. After 1 hour of stirring, the reaction mass turned yellow-green. After completion of the reaction (about 4 hours), the mixture was vigorously poured into chilled methanol and the solution was refrigerated. After 24 hours, the precipitate was separated on a funnel with a filter bottom, washed several times with cold methanol. The precipitate was dried in vacuum. As a result, a mixture of substances weighing 25 g was obtained. Based on the characteristic spots on the thin-layer chromatogram (eluent petroleum ether: methylene chloride 2:1), it was concluded that a mixture of 2,3,6,7,10,11-hexapentyloxytriphenylene and 2-hydroxypropyloxy-3,6,7,10,11-pentapentyloxy-triphenylene.

Synthesis of 2-hydroxypropyloxy-3,6,7,10,11-pentapentyloxytriphenylene.

The resulting mixture of substances was placed in a 250 ml three-necked flask and added 60 ml. acetone. Then, 8 g of 3bromopropanol-1 and 7.5 g of potassium carbonate were introduced into the reaction flask. The flask was filled with argon. The reaction mixture was heated with stirring for 12 hours. Potassium carbonate was filtered off, washed with methylene chloride and methanol, the main and washing solutions were combined, and the solution was evaporated, as a result of which a dark violet mass was obtained. Isolation of 1-hydroxypropyloxy-2,5,6,8,9-pentapentyloxytriphenylene was carried out using a chromatographic column using silica gel 60 (63-200 microns) as an adsorbent, and ethyl acetate: petroleum ether in a ratio of 1:4 as an eluent (to separate 2,3,6,7,10,11-hexapentyloxytriphenylene), and then in a 1:1 ratio (to wash out 2hydroxypropyloxy-3,6,7,10,11-pentapentyloxytri-phenylene from the column). After evaporation of the solution, dark violet oil was obtained, cold methanol was added to it and put in the refrigerator for a day. Then the precipitate was filtered off and dried in vacuo. As a result, a white substance weighing 7.5 g was obtained. Melting point 104 °C. Yield 30.3%.

Synthesis of 2-(acryloyloxypropyloxy)-3,6,7,10,11-pentapentyloxy-triphenylene.

Into a 250 ml round bottom flask 7.5 g of 1-hydroxypropyloxy-2,5,6,8,9-pentapentyloxytriphenylene, crystalline 2,6ditretbutyl-p-cresol, 10 ml, were placed in methylene chloride, 0.18 ml ethylene carbonyl halide and 0.24 ml triethylamine. After all the starting materials were added to the flask, another 10 ml of methylene chloride was added. The reaction was carried out with stirring and heating for 12 hours. After 12 hours of heating, the dark blue reaction mixture was poured into well-chilled water (with pieces of ice). Next, 50 ml was added to this mixture. methylene chloride and the whole mixture was transferred to a separatory funnel, to which dry sodium bicarbonate was added, dissolving it in the introduction layer. The organic layer was separated, and the aqueous layer was washed with methylene chloride, the basic and washing solutions were combined, the entire organic layer was washed with water three times and dried over sodium sulfate. The solution was evaporated, ethanol was added to the remaining dark purple oil and left in the refrigerator for a day. Light violet crystals were filtered off and dried in vacuo. Then, the substance was purified twice on a chromatographic column (eluent -ethyl acetate : petroleum ether 1:1). The result was a white substance weighing 3. The synthesis of 2,4,7-trinitro-9-fluorenylidene-aminooxy)propionic acid (TNF-carb) described in [27] was performed according to the scheme. We mixed 10 g (25.5mmol) of TNF (TCC, Japan) and 4.5g (26 mmol) of the alkylated oxime in 100 ml of acetic acid with 0.75 g (38.5 mmol) of 4-toluenesulfonic acid monohydrate as catalyst. Hydrolysis of the corresponding ester and twofold recrystallization from acetone yielded 8.5 g (85 %) of the product: Tm = 203 oC; IR(KBr): ν= 1700 cm-1 (C=O). 1H NMR (400 MHz, acetone -d6): δ (ppm) = 9.34 and 9.11 (2s; 1H, H3), 8.95 and 8.88 (as, 1H, H1), 8.70 and 8.58 (2s, 1H, H8), 8.54 and 8.43 (2d, 1H, H6), 8.28 and 8.18 (2d, 1H, H5), 4.90 (t; 2H, N-OCH2), 3.02 (t; 2H, CH,-CO-OH). Microanalysis: calculated C -47.77 %, H -2.51 %, N-13.93 %; found C-47.80 %, H-2.50 %, N -13.90 %.

Preparation of blends.

The complexes were obtained by mixing H5T and TPh-3A with TNF-carb in 4:1 molar proportion in THF. In addition H5T/TNFcarb were also prepared in 2:1 and TPh-3A/TNF-carb in 2:1, 3:2, 2:3 and 1:1 molar proportions for FTIR measurements. The mixtures was subsequently evaporated to dryness at room temperature. To remove any traces of solvent and to ensure the correct phase behavior, the resulting composites were heated up to the isotropization temperatures, and then cooled slowly.

Characterization methods Film preparation. The films were prepared by spin-coating on Si substrates with the help of a spin-150 machine (APT, Germany) from solution in THF with 20 mg/ml concentration at 1000 rot/min speed with acceleration of 500 rot/s2. DSC measurements were carried out with Mettler DSC 823E (Mettler Toledo, Switzerland) using 40 μl Al pans.at a heating rate of 10oC/min under argon atmosphere. Melting points and enthalpies of indium and zinc were used for temperature and heat capacity calibration. Polarization Optical Microscopy (POM). The optical textures and thermal transition temperatures were evaluated with the help of a polarizing optical microscope equipped with a Mettler Toledo FP-82 HT hot stage and a microprocessor temperature control unit. The temperature of the tested samples was maintained with an accuracy of 0.1 °C. Samples were placed on microscope slides (Fisherbrand, Fisher Scientific, USA) and covered with cover slips. The slides were used as received. The heating/cooling rate was 5oC/min. GIWAXS experiments were performed on the BM26 beamline of ESRF (Grenoble, France) using the photon energy of 12 keV (wavelength -1.04 Å). The 2D data were collected at an incidence angle of 0.2° using a FReLoN 2k CCD detector with sampletodetector distance of ca. 133 mm. The modulus of the scattering vector s (|s| = 2sinθ/λ, where θ is the Bragg angle) was calibrated with 7 orders of silver behenate. The 1D reduction of the data and fitting was performed with home-made routines built in Igor Pro (Wavemetrics Ltd.).

FTIR spectra were recorded with IFS 66 v/s (Bruker, Germany) (30 scans, resolution 1.0 cm-1, wavelength range 400 -4000 cm-1). Samples were prepared in the form of thin layers squeezed between two KBr optical glasses. Thin layers were obtained from THF solutions after solvent evaporation.

Conclusions

In the present work, we have investigated new complexes of triphenylene discotics, namely, 2,3,6,7,10,11 -hexakis(pentyloxy) triphenylene (H5T) and 2-(acryloyloxypropyloxy)-3,6,7,10,11-pentapentyloxy-triphenylene (TPh-3A), with an electron acceptor, β-(2,4,7-trinitro-9-fluorenylideneaminooxy) propionic acid (TNF-carb). One of the discotics is a well-known H5T, whereas the second one is a H5T-modified acrylic monomer-TPh-3A. In both cases, a new electron acceptor TNF -carb is used. Our studies by means of grazing-incidence X-ray diffraction and FTIR spectroscopy are focused on establishing the structure of the complexes and evaluating the impact of structural modification of the discotic constituents on the complex formation. Based on the results of synchrotron GIWAXS experiments, we found that constituent discotics crystallize in orthorhombic unit cells whereas complexation of H5T and TPh-3A with TNFcarb results in a double gyroid and hexagonal phases, respectively. Modelling of the double gyroid phase makes us supposing that the TNF-carb acceptor occupies the nodes of the double gyroid structure while the H5T molecules are located in the struts forming triple junctions at each node. For the hexagonal crystal of the TPh-3A /TNF-carb complex, the acceptor molecules are likely located in the interstices between the neighboring supramolecular columns of TPh-3A. It can be then concluded that even a small modification in the structure of H5T can result in a significant variation of the structure of its complex with TNF-carb. In particular, addition of a relatively small but asymmetric 2-(acryloyloxy-propyloxy) group on one of the alkyl arms of H5T makes dramatically changes the symmetry of the phase. The described impact of a small substituent on the final supramolecular structure can be accounted for by its H-bonding with the carboxylic group of TNF-carb. The molecular structures of the blends were explored by means of FTIR spectroscopy. A detailed FTIR spectra analysis illustrates fine changes in inter-molecular bonds. The initially dimerized acceptor molecules totally collapse in the complex structures whereas additional H-bonds between the carboxylate group in TNF-carb and the ester group of TPh-3A contribute in the formation of TPh-3A/TNF-carb complex. At room temperature, the triphenylene -based compounds H5T and TPh-3A crystallize in orthorhombic unit cells. The complexes with TNF-carb reveal different structures from those of the pristine discotics. As shown with FTIR, the donoracceptor interaction binding the nitrogen atoms of nitro groups and electron-deficient carbon atoms in the aromatic cores as well oxygen atoms in the ether groups is the same in both complexes. Hydrogen bonds between the hydrogen atom in carboxylate group of TNF-carb and oxygen atom in the alkoxy-group in the discotic molecule participate in binding as well. However, the latter bond is less pronounced in TPh-3A containing system. At the same time, the ester group in TPh-3A forms an additional H-bond with carboxylate group in TNFcarb. The difference between molecular structures of the complexes may be a possible reason for the change in the phase structure types when instead of H5T TPh-3A molecules contribute in the complex formation. The conclusions section should come in this section at the end of the article, before the acknowledgements.

Figure 1 .

 1 Figure 1. Structures of HAT5, TPh-3A and TNF-carb.

Figure 2 .

 2 Figure 2. DSC curves of H5T (a) and TPh-3A (b) recorded during heating and cooling at 10 deg/min.

Figure 3 .

 3 Figure 3. POM images of H5T at RT (a) and 88.4 oC (c) and TPh-3A at RT (b) and 80 oC (d).

Figure 4 .

 4 Figure 4. Room-temperature 2D GIWAXS patterns recorded on thin films of H5T (a), TPh-3A (b), H5T/TNF-carb (4:1) (c), and TPh-3A/TNF-carb (4:1) (d).

Figure 5 .

 5 Figure 5. POM images of H5T/TNF carb (a) and TPh-3A/TNF carb (b) blends at RT.

Figure 6 .

 6 Figure 6. Comparison of IR spectra a: TNF-carb and Н5Т/TNF-carb and b: (4:1) blends of H5T/TNF-carb and TPh-3A/TNF-carb.

  shift of the stretching band νC=O in C(O)OH towards long wavelength down to 1703 cm-1. The associates of such a kind usually show several weak bands in 2800-2400cm-1 wavelength range, and the number and intensities of those bands depend on the local symmetry of the associate [23]. The dimer associate shown in Scheme 1 has local symmetry high enough

Figure 7 .

 7 Figure 7. Comparison of IR spectra of TPh-3A/TNF-carb blends of different compositions. 1-4:1, 2 -3:2, 3 -1:1, 4 -2:3

Figure 8 .

 8 Figure 8. Hypothetic structures of H5T/TNF-carb (a) and TPh-3A/TNF-carb (b) at RT. For the sake of clarity, the triphenylene cores of TPh-3A are marked in dark blue. Hydrogen bonds are shown in panel (a) with red dashed lines.

1 .

 1 Synthesis of a mixture of 1-hydroxy-2-pentyloxybenzene and 1,2-dipentyloxybenzene.

FeCl 3

 3

  2 g. Yield 16%. The melting point is 68.1 °C, the isotropization temperature is 97.9 °C. Identification of the obtained monomer was carried out by 1H NMR spectroscopy (CDCl3): δ (ppm) 7.84 + 7.81 (6H, Ar-H), 6.42 (d, 1H, COCH = CH2), 6.13 (dd, 1H , COCH = CH2), 5.81 (d, 1H, COCH = CH2), 4.47 (t, 2H, OCH2 (CH2) 2OCO), 4.31 (t, 2H, O (CH2) 2CH2OCO), 4 21 (t, 10H, OCH2 (CH2) 3CH3), 2.00-1.86 (m, 10H, OCH2CH2 (CH2) 2CH3), 2.36-2.22 (m, 2H, OCH2CH2CH2O), 1, 65-1.35 (m, 20H, OCH2CH2 (CH2) 2CH3), 1.1-0.8 (t, 15H, OCH2CH2 (CH2) 2CH3). The NMR results are in good coincidence with the theoretical spectrum and data reported in [26]. III. Synthesis of 2,4,7-(Trinitro-9-fluorenylideneaminooxy) propionic acid (TNF-carb).

Table 1 .

 1 Experimental and calculated diffraction peaks positions at room

temperature Н5Т hkl/d- spacing, Å Н5Т Fit, Å Н5Т/TNF- carb hkl/d- spacing, Å Н5Т/TNF- carb fit, Å ТРh-3A hkl/d- spacing, Å ТРh-3A, fit, Å ТРh-3A/TNF- carb hkl/d- spacing, Å ТРh-3A/TNF- carb fit, Å

	200/		211/		200/		110/
	16.4	16.4	14.8	14.9	16.8	17.0	15.6	15.5
	020/		220/		400/		200/
	13.2	13.3	12.6	12.9	8.7	8.6	13.7	13.7
	220/		321/		020/		020/
	10.3/	10.3	9.6	9.8	13.5	13.6	13.9	13.7
	230/		Intra-stack/		220/		001/
	8.0	7.9	3.5		10.7	10.7	3.5	3.5
	001/				420/		101/
	4.8	4.7			7.4	7.3	3.4	3.4
	211,221/				210/		201/
	4.5	4.6			14.4	14.4	3.4	3.4
					410/
					8.3	8.2
					230/
					8.2	8.2
					610
					5.7	5.6
					001/
					4.5	4.5
					021/
					4.2	4.2
					001/ 4.6	4.6
					211/ 4.4	4.4
					221/ 4.2	4.2
					231/ 4.0	4.0

Table 2

 2

	Absorption range, сm -1	Assignment	TNF-carb	H5T	Absorption bands (сm TPh-3A	-1 ) H5T/TNF-carb	TPh-3A/ TNF-
							carb

. Comparison of the major absorption bands in IR spectra of initial components and their blends of 4:1 (H5T/TNF-carb and TPh-3A/TNF-carb)

Acknowledgements

The work of the TIPS RAS was carried out within the State Program of TIPS RAS. The MSU team acknowledges financial support from the Ministry of Science and Higher Education of the Russian Federation within State Contract 075-15-2019-1889.

Author Contributions

Conflicts of interest

There are no conflicts to declare.