Juan Ángel Sans

Dr Rosario Vilaplana

E Lora Da Silva

Dr Catalin Popescu

Dr Vanesa P Cuenca-Gotor

Dr Adrián Andrada-Chacón

Dr Javier Sánchez-Benitez

Dr Oscar Gomis

Prof. F André L J J Pereira

Plácida Rodríguez-Hernández

Juan Ángel Sans

Estelina Lora

Da Silva

Vanesa Paula Cuenca-Gotor

André Luis

Jesus Pereira

Alfonso Muñoz

Dr Dominik Daisenberger

Dr Braulio García-Domene

Alfredo Segura

Daniel Errandonea

Ravhi Kumar

Oliver Oeckler

Philipp Urban

Dr Julia Contreras-García

Dr Francisco J Manjón

Dr J A Sans

Manjón

Prof P Rodríguez-Hernández

Prof A Muñoz

Prof A Segura

Prof. D Errandonea

Prof R Kumar

Prof O Oeckler

Characterization and decomposition of the natural van der Waals SnSb2Te4 under compression

Keywords: metavalent bonding, high pressure, pressure-induced decomposition, electronic topological, bonding character

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The search for topological features in materials including topological insulators (TIs) and topological superconductors (TSs) is currently one of the hot topics in the Material Science field because of its interest in fundamental physics and applications in spintronics and quantum computation. [1][2][3] Recently, several tools have been designed to identify theoretically-predicted TI candidates and create an extensive database of compounds that exhibit these properties, [4][5][6] defining respective limitations and filters required by theoretical calculations to avoid falsepositive predictions. [7] The discovery of 3D-TI properties in layered tetradymite-like A2X3 compounds, such as Bi2Te3, Bi2Se3 and Sb2Te3 compounds [3,8,9] and the trivial insulating behavior of Sb2Se3 [10] have opened the question about which is the electronic and structural origin and the limiting factors of this conduct, compared to other similar materials, such as the layered tetradymite-like BA2X4 compounds.

Binary A2X3 layered compounds are usually p-type semiconductors with a narrow gap, leading to a high electrical conductivity. [11] In particular, -Sb2Te3 and -Bi2Te3 are the best thermoelectric materials near room temperature found to date, [START_REF] Rowe | CRC Handbook of Thermoelectrics[END_REF][START_REF] Venkatasubramanian | [END_REF] since they feature a very small thermal conductivity. Additionally, the hybridization between the valence and the conduction band states favored by a large spin-orbit coupling (SOC) and a small bandgap, leads to the formation of Dirac cones in the electronic band structure that is responsible for their 3D-TI properties. [8] The TI properties observed in A2X3 binary compounds with layered tetradymitelike R3 m structure [space group (s.g.) 166, Z=3] have triggered the exploration of ternary BA2X4 compounds based on those materials. [8,[14][15][16] These ternary compounds are expected to show richer physics than their binary counterparts, plus the possibility to tune their properties in a finer way by selecting appropriate B atoms. In fact, 3D-TI behavior has been predicted in many BA2X4 compounds [11,[14][15][16][17][18][19] and rhombohedral SnSb2Te4 with layered tetradymite-like structure has been found to be a p-type 3D-TI. [11] The tetradymite-like structure of binary A2X3 compounds is a 2D layered structure formed by blocks composed by five layers (X1-A-X2-A-X1) and called quintuple layer (QL), being A and X the cation and the anion, respectively, and X1 and X2 the two non-equivalent anions in the unit cell. These QLs pile up along the trigonal c axis and are traditionally considered to be linked by van der Waals (vdW) forces leading to the 3D material. [8] In ternary BA2X4 compounds the tetradymite-like R3 m structure is formed by replacing the central anion (X2) of A2X3 compounds with a three-atoms sub-block (X2-B-X2). In this way, the block is composed of seven layers (X1-A-X2-B-X2-A-X1) and called septuple layer (SL). [20] In these ternary compounds, the tetradymite-like structure can be described by two octahedra formed by A and B cations surrounded by six X1/X2 and X2 anions, respectively. In fact, these ternary compounds with tetradymite-like layered structure define a new family of materials, named "natural van der Waals heterostructures", whose nanosheets promise novel and interesting properties. [21] Due to their technological interest, the thermoelectric properties of some layered tetradymitelike BA2X4 compounds have been studied [21][22][23][24][25] and experimental results have shown that there is a certain disorder in the crystal structure. [17,[26][27][28][29][30][31] In particular, SnBi2Te4 and SnSb2Te4 are the BA2X4 materials showing the smaller cation exchange in their atomic sites. [23,31,32] Noteworthy, some BA2X4 compounds, like rocksalt-type SnSb2Te4 and GeSb2Te4, have revealed strong properties as phase change materials since they are able to rapidly change between an amorphous and a crystalline state by light irradiation or current application. In particular, SnSb2Te4 crystallizes predominantly in the rhombohedral R3 m structure (s.g. 166, Z=3) while a smaller fraction crystallizes in the metastable rocksalt-type Fm3 m structure (s.g.

225, Z=4

). Additionally, it can be stabilized in an amorphous phase with average octahedral coordination in the short-range order. [33] It must be stressed that both polymorphs of SnSb2Te4 (also GeSb2Te4) and its binary parent compounds, rhombohedral R3 m -Sb2Te3 and rocksalttype Fm3 m SnTe (c-SnTe), do not accomplish the Lewis-octet rule. Consequently, some of them have been proposed to be incipient metals by showing the recently discovered metavalent bonding; [34][35][36][37] a matter still under debate. High pressure (HP) studies have been conducted in rocksalt-type SnSb2Te4 and GeSb2Te4 [38] and in rhombohedral SnBi2Te4. [39] A pressure-induced amorphization (PIA) was reported in rocksalt-type SnSb2Te4 (GeSb2Te4) upon compression above 11 (15) GPa, [38] whereas a pressure-induced electronic topological transition (ETT) has been suggested to occur in rhombohedral SnBi2Te4. [39] Despite these efforts, many questions have yet to be addressed for the rhombohedral BA2X4 compounds and in particular for SnSb2Te4, including its recently proposed superconducting character at HP. [40] For instance, "how does the presence of the new SnTe6 octahedron in rhombohedral SnSb2Te4 affect the properties of the host Sb2Te3 structure?" and "how does rhombohedral SnSb2Te4 behave under compression?". In this scenario, we wonder if pressure on rhombohedral SnSb2Te4 leads to: i) a simple compression of the material remaining in the original structure; ii) an isostructural phase transition (IPT) followed by a structural phase transition (PT) towards a different structure, like in its parent compound Sb2Te3; iii) an ETT, similar to its counterpart SnBi2Te4; iii) a PIA, reported in rocksalt-type SnSb2Te4; or even iv) a pressure-induced decomposition (PID).

In this work, we report the room-temperature structural, vibrational and electrical properties of SnSb2Te4 under compression from an experimental and theoretical point of view by means of angle-dispersive X-ray diffraction (ADXRD), Raman scattering (RS) and transport measurements complemented with DFT ab-initio calculations and a thorough analysis of the electron density. We will show the good agreement between both experimental and theoretical descriptions and a comparison of the behavior of this material under compression has been compared to that of its parent binary compounds (-Sb2Te3 and c-SnTe). We will pay special attention to the evolution of the interlayer vdW interaction under compression, considering this feature the key element to understand the behavior of the c/a ratio under compression and the stability pressure range of its low-pressure (LP) phase. Moreover, we will demonstrate that SnSb2Te4 undergoes a pressure-induced IPT near 2 GPa followed by a PID above 7 GPa. The contextualization of this result on the framework of the ternary BA2X4 compounds can shed light on their behavior under compression. Finally, we will show that the RS of SnSb2Te4 and its comparison with the theoretical vibrational properties of SnSb2Te4 and those of its parent compounds has revealed that: i) there is a Fermi resonance around 3.5 GPa, similar to what occurs in c-SnTe, and ii) the Raman spectrum of SnSb2Te4 shows some vibrational modes similar to those of forbidden c-SnTe. This result evidences a novel procedure to experimentally observe the forbidden vibrational modes of some materials. Finally, we will analyze the electronic topology of the different bonds found in SnSb2Te4 together with its evolution under pressure and show that this compound behaves like the recently proposed incipient metals.

RESULTS AND DISCUSSION

2.1. X-ray diffraction under pressure

LP phase

As already commented, SnSb2Te4 usually crystallizes in rhombohedral R 3 m polymorph following a GeSb2Te4 structure-type with four atoms at the independent Wyckoff sites (Sn at 3a and Sb, Te1 and Te2 at 6c). A clear scheme of the polyhedral arrangement for the GeSb2Te4type structure is shown in Figure 1, together with a description of the different layers composing this compound. The experimental ADXRD pattern at room conditions (see Figure S1 in Supplemental Material (SM)) has been fitted with a von Dreele-type Le Bail refinement, which yields a trigonal unit-cell volume of 662.7(7) Å 3 with lattice parameters a= 4.2977(1) Å and c= 41.43(4) Å. These values are in good agreement with those reported in the literature and obtained from theoretical simulations (see Table 1).

Two ADXRD experiments were carried out by employing helium (up to 37 GPa) and silicone oil (up to 12 GPa) as a pressure-transmitting medium (PTM). The latter experiment up to 12 GPa (experiment 2) was performed in order to conduct a more detailed study of the LP phase.

ADXRD patterns of SnSb2Te4 at different pressures from experiment 2 are shown in Figure S1 in SM.

In Figure S1 it is possible to observe a clear shift of the Bragg reflections of the LP phase of SnSb2Te4 towards higher 2θ angles with increasing pressure. This feature occurs due to the monotonous decrease of the distances between crystallographic planes with compression. A clear change in the diffraction patterns above 7 GPa suggests that the LP phase is no longer stable. We want to stress here that the lack of Rietveld refinement of our measurements prevents us from obtaining the experimental atomic positions in SnSb2Te4. Consequently, we have used the atomic positions of our calculations to discuss the pressure dependence of many parameters in order to understand the behavior of SnSb2Te4 under compression. The good agreement between the experimental and theoretical pressure dependence of the unit cell volume, lattice parameters and the c/a ratio discussed in the following paragraphs, assures us of the accuracy of our theoretical data for further considerations.

The pressure dependence of the experimental and theoretical unit cell volume and lattice parameters of SnSb2Te4 of the two experiments is displayed in Figures 2a and2b, respectively. The slight discrepancy observed in both figures between the values obtained using helium and silicone oil as PTM can be explained by the typical pressure uncertainty in these experiments (~ 0.5 GPa). The experimental unit cell volume (of both experiments) was fitted to a third-order Birch-Murnaghan equation of state (BM-EoS) with a B0' higher than 4, as suggested by the positive trend of the F-f plot calculated from EoSFIT. [41] The experimental BM-EoS (see Figure 2a) yields a zero-pressure unit cell volume, V0, and bulk modulus, B0, of 663.1(6) Å 3 and 31.6(4) GPa, respectively. These values are in good agreement with our calculations (see Table 1).

The similar features of the layered structure of SnSb2Te4 and its parent binary compound -Sb2Te3 suggests that the compressibility of the former must be related to that of the latter.

More precisely, the compression of the former should be a combination of the compression of the SbTe6 polyhedral units, also present in -Sb2Te3, and of the SnTe6 polyhedral units (a quasiregular SnTe6 octahedron) in the center of the SL, also present in c-SnTe compound. This hypothesis is supported by the similar volume compressibility of both SnTe6 and SbTe6 octahedral units in SnSb2Te4 and those occurring in its two parent binary compounds as shown in Figure S2 in SM.

The evolution of the theoretical interatomic distances of SnSb2Te4 at HP (Figure S3 in SM)

shows that the Sn-Te interatomic distance inside the quasi-regular SnTe6 octahedron compresses at a similar rate than the Sn-Te distances in c-SnTe (B0≈ 50 GPa). [42] Since the Sn-Te distance is the second less compressible interatomic distance of the SnSb2Te4 structure, it can be assumed that the compressibility of SnSb2Te4 is mostly determined by the compressibility of -Sb2Te3. This hypothesis is confirmed by both experimental and theoretical data, shown in Table 1. Note that -Sb2Te3 shows an experimental average B0 of 36.1(9) GPa [43] that is in very good agreement with the experimental bulk modulus of SnSb2Te4. In conclusion, the compressibility of SnSb2Te4 is dominated by the -Sb2Te3 component due to harder behavior of the intercalated SnTe6 octahedron.

The experimental B0 of SnSb2Te4 is similar to that of the isostructural compound SnBi2Te4 (B0= 35(2) GPa). [39] This result implies that the compressibility of these two layered BA2X4 compounds is almost independent of the A cation and fully dependent on geometrical factors of the layered structure. A close look at the pressure dependence of the theoretical interatomic distances in Figure S3 shows a much larger compression of the Te1-Te1 interlayer distance than that found for the Sn-Te and Sb-Te intralayer distances. Therefore, the bulk compressibility of SnSb2Te4 (also for SnBi2Te4) is dominated by the compressibility of the vdW gap between the SLs. The compressibility of the Te1-Te1 interlayer distances is similar for both SnSb2Te4 and -Sb2Te3, in good agreement with the similar bulk compressibilities of both compounds, shown in Table 1. In conclusion, the compressibility of SnSb2Te4 is dominated by the strong compression of the Te-Te interlayer distance, assumed to be governed by vdW interactions, and consequently is similar to that of -Sb2Te3 and SnBi2Te4.

Regarding the evolution of the experimental and theoretical lattice parameters at HP (see Figure 2b), they can be fitted to a modified BM-EoS in order to reproduce their sub-linear behavior. Table 2 summarizes the axial bulk modulus, B0i, and the axial compressibility as 𝜅 = obtained for each lattice parameter. At room conditions, 𝜅 ~ 2𝜅 is consistent with the much larger compression of the Te1-Te1 interlayer distance along the c-axis than the Sn-Te and Sb-Te intralayer distances in the a-b plane (Figure S3). Such a hypothesis is further substantiated by the evolution of the different interplanar distances along the c-axis (see Figure S4), which allows us to identify the different contributions to the compressibility of the c-axis.

The strong reduction of the interplanar compressed Te1-Te1 distance when compared with the behavior of the overall interplanar distances corroborates that the Te1-Te1 interplanar distance dominates the compression along the c-axis. Moreover, a fit of the interplanar Te1-Te1 distance with a modified BM-EoS yields a bulk modulus of 21 (1) GPa that is similar to that of the c-axis (23.8(4) GPa). Therefore, we can conclude that the interplanar Te1-Te1 distance, assumed to be determined by the vdW interaction, is the main source for the compressibility of the unit cell along the c-axis and that the stronger reduction of the Te1-Te1 distance than the Sb-Te1 or Sb-Te2 distance is also the responsible for the much larger compressibility along the c-axis than along the a-axis.

Additional support to the interpretation provided in the previous paragraph is obtained by comparing the experimental and theoretical B0i and i of SnSb2Te4 with those of SnBi2Te4 [39] and -Sb2Te3 [43,44] presented in Table 2. The close similarity of the values of the B0i and i in the three compounds supports the presence of similar mechanisms of compression and a similar strength of the interatomic interactions in all of them.

It is noteworthy of mentioning that the compression of the c-axis in SnSb2Te4 does not imply a compression of all the interplanar distances along the c-axis. Despite the decrease of the Sb-Te1 interatomic distance for SnSb2Te4 (see Figure S3), the interplanar Sb-Te1 distance expands under compression and the same occurs for -Sb2Te3 (see Figure S4). This feature clearly suggests an increase of the angle between the ab-plane and the Sb-Te1 bond at HP that distorts the SbTe6 octahedron as clearly observed in Figure S5a in SM. We also intend to highlight that although the Sb-Te1 interatomic distance shows the same pressure dependence in SnSb2Te4 and -Sb2Te3, the presence of the short Sn-Te bond in SnSb2Te4 triggers a slight increase of the Sb-Te2 interatomic distance, and a consequent larger decrease of the Sn-Te bond with pressure than in c-SnTe. This result means that there is a slightly larger and weaker Sb-Te2 bond in SnSb2Te4 than in -Sb2Te3. This variation caused by the chemical pressure induced by the combination of the binary parent compounds (c-SnTe and -Sb2Te3) in the formation of SnSb2Te4, can also be understood through the change in the orientation of the lone electron pair (LEP) of Sb, which can induce a slight distortion of the SbTe6 polyhedral unit. This distortion is small because the compressibility of the Sb-Te2 interatomic distance for both SnSb2Te4 and -Sb2Te3 compounds follows a similar pattern.

A good agreement between experimental and theoretical data is also found for the evolution of the c/a ratio at HP (see the inset of Figure 2b). This ratio shows a clear change of tendency above 2 GPa similar to that observed in -Sb2Te3 [43,44] and SnBi2Te4. [39] The minimum of the c/a ratio in SnSb2Te4 can also be explained by analyzing the pressure dependence of respective interplanar distances along the c-axis (see Figure S4). In particular, the evolution of the Te1-Te1 interplanar distance in SnSb2Te4 shows a strong (normal) compression below (above) 2 GPa. This behavior is typically associated with the weak character of the vdW bonds at LP and its hardening due to the increase of the covalent character of the Te-Te bonds at HP. [45] A similar conduct of the c/a ratio is observed for -Sb2Te3 since the Sb-Te interplanar distances evolve in this compound in a similar manner as in SnSb2Te4 (see Figure S4). Therefore, we can conclude that the change of the compression rate of the interlayer space (caused by the change of the compressibility of the Te1-Te1 interplanar distance) gives rise to the c/a ratio minimum observed in SnSb2Te4 and -Sb2Te3. The evolution of the vdW character of the interlayer bonds at HP will be addressed in depth later on, when we discuss the analysis regarding the dependence of the electronic topology at HP. The big change in the slope of the c/a ratio in SnSb2Te4 and related compounds at HP is likely related to a pressure-induced IPT. We must recall that these chalcogenides are mainly composed by group-15 cations acting with their lowest valence state and featuring a strong cationic LEP stereoactivity that has a deep effect in the formation of the 2D layered structure. The presence of the cationic LEP modifies the electronic distribution of the charges in the crystal and distorts the geometry of the bonds. Moreover, the cationic LEP is mainly oriented along the c-axis in these compounds and contributes to the vdW interaction between the layers and to the strong compressibility of the c-axis at LP since the LEP is extremely compressible at LP. This scenario has been already observed in a number of group-15 sesquichalcogenides. [46,47] Additionally, it has been widely reported that both the cationic LEP and the vdW interaction become more incompressible at HP due to the progressive decrease of the LEP activity and the increase of the strength of the interlayer forces. Therefore, it can be considered that these changes in compressibility of electronic 'density-clouds' at relatively LP lead to a new isostructural phase with a different c/a ratio in SnSb2Te4 and related chalcogenides, and these can be understood as an IPT of electronic origin, as we will further show.

A different way of understanding the structural behavior of SnSb2Te4 at HP is by studying the compression of the two octahedral units forming the SnSb2Te4 heterostructure: the regular octahedron around Sn and the slightly deformed octahedron around Sb (see Figure 1). Figure S6 in SM shows the evolution of the theoretical quadratic elongation of both octahedra at HP. This parameter was defined by Robinson et al [48] to analyze the distance of the inner atom of a polyhedron with respect to the central position, which is an indirect measurement of the irregularity of the polyhedral unit. In our case, the SnTe6 (SbTe6) octahedron shows practically no changes in the quadratic elongation up to 2 GPa and an increase above 2 (4) GPa. This result suggests that both octahedra are almost insensitive to pressure while there is a strong compression of the vdW interlayer gap below 2 GPa. Nevertheless, SnTe6 octahedra show a considerable increase of the polyhedral distortion above 2 GPa; once the vdW gap becomes as incompressible as the octahedral units. Therefore, results of Figures S5 and S6 support the occurrence of a pressure-induced IPT near 2 GPa in SnSb2Te4.

Finally, in order to measure the differences of the interatomic distances in both octahedra with respect to those in a regular coordination, we have plotted in Figure S7 the evolution of the theoretical distortion index of both octahedra at HP. [49] It can be observed that the regular SnTe6 octahedron remains regular during the whole compression process while the distorted SbTe6 octahedron becomes slightly more regular under compression. This is a consequence of the evolution of the Sb-Te1 and Sb-Te2 distances under compression, which tend to follow a similar pattern, but at a smaller rate. In summary, we have shown that the own definition of the SnSb2Te4 heterostructure as a layered distribution of SLs makes it essential to analyze the polyhedral units and the inter-and intra-layer compressibility in order to understand respective behavior at HP.

To close this section, we have plotted the experimental quadratic elongations of the AX6 and BX6 octahedra of all BA2X4 compounds known to have the R3 m structure at room pressure according to the ICSD database (see Figure 3). In this way, we can try to shed light on the HP behavior of the compounds of this ternary family. It can be observed that SnSb2Te4 is one of the compounds with the smallest quadratic elongation of the AX6 octahedron (SbTe6) and conversely with the largest quadratic elongation of the BX6 octahedron (SnTe6). Therefore, according to the trend observed in the theoretical quadratic elongation of both octahedra at HP (see Figure S6), it can be deduced that SnSb2Te4 will behave at HP similar to PbSb2Te4 at LP, while SnBi2Te4 tends to behave at HP as GeSb2Te4 at LP.

Regarding the Figure 3, more conclusions can be drawn. A priori, it could be thought that the AX6 quadratic elongation should decrease in the sequence As-Sb-Bi due to the larger stereoactivity of the LEP in As than in Sb and Bi. This fact is due to the stronger hybridization of the cationic s-p levels in As than in Sb and Bi for a given atom. [50] On the other hand, it could be also thought that the BX6 quadratic elongation should decrease in the sequence Pb-Sn-Ge due to the larger difference between the s-p levels in Pb than in Sn and Ge. [50] Unexpectedly, the above arguments seem not to be true since SnBi2Te4 (with a common B cation with SnSb2Te4) has a larger AX6 quadratic elongation, whereas GeSb2Te4 (with a common A cation with SnSb2Te4) has a smaller BX6 quadratic elongation and a much larger AX6 quadratic elongation. Therefore, results of Figure 3 suggest that there is a close relationship between the quadratic elongation of the AX6 and BX6 octahedra in these compounds and that not all combinations of AX6 and BX6 quadratic elongations compatible with the R3 m structure. This hypothesis is supported by the lack of compounds PbAs2Te4 and SnAs2Te4 with R3 m structure, which should be located in the upper right region in the diagram; i.e. far away from the red line marking the average of the possible AX6 and BX6 quadratic elongations. A similar reasoning can be applied to explain why PbSb2Se4, SnSb2Se4, PbBi2S4 and SnSb2S4 cannot crystallize in the R3 m structure. [51][52][53] In this context, it must be recalled that the LEP activity of group 15 cations increases when the anion follows the sequence Te-Se-S-O. [50] Therefore, taking into account the energetic difference between the p-levels of the anion and the s-levels of the cation, the strong LEP stereoactivity of As in tellurides should be similar to that of Sb cation in selenides and sulfides and to that of Bi in sulphides and oxides, taking into account the energetic difference between the p-levels of the anion and the s-levels of the cation. Consequently, this strong cation LEP stereoactivity allows us to explain why the above-mentioned compounds do not crystallize in the R3 m phase.

Pressure-induced decomposition (PID)

Above 7 GPa, a clear change of the experimental XRD patterns occurs. The disappearance of Bragg reflections around 11 and 14.6 degrees and the appearance of new peaks at 8.6 and 10.1 degrees (at 10.8 GPa) without showing a relevant peak broadening suggests the absence of a PIA. Thus, the only two possibilities are a PT or a PID.

In order to probe possible crystalline HP phases after a PT, we have resorted to the structure field map of BA2Te4 compounds reported by Zhang et al., [54] with ternary compounds systematically ordered according to the cationic orbital radii, RB and RA. [55] This structure field map (see Figure 4) allows us to understand and predict the structures of ternary BA2Te4 compounds at LP by knowing RB and RA. Moreover, it can help in predicting the HP phases if we know how orbital radii behave at HP. In the field map of Zhang et al., materials with RB ∈ [1.6, 1.9] a.u. and RA ∈ [1.0, 2.0] a.u. crystallize in the b37 structure (s.g. R3 m); however, new tellurium-based ternary chalcogenides formed by different group-14 B cations (B = Ge, Sn and Pb) group-15 A cations (A = As, Sb and Bi) also crystallize in s.g. R3 m according to the ICSD database. This are the cases of GeAs2Te4 (with RB=1.415 a.u. and RA=1.560 a.u.) and PbBi2Te4 (with RB=1.997 a.u. and RA=2.090 a.u.). We have included these two compounds in the structure field map because they limit the new borders of materials with s.g. R3 m. In this way, we can extend the stability ranges of the b37 structure to RB ∈ [1.4, 2.0] a.u. and RA ∈ [1.0, 2.1] a.u. with respect to the structure field map reported by Zhang et al. [55] The new structure field map of BA2Te4 compounds allows us to consider several possible HP phases for a compound with an initial R3 m structure. The most important ones are the spinel b4 structure (s.g. P4 2m or I4 ) and the monoclinic d3 structure (s.g. C2/m). It is noteworthy to highlight that one of the parent binary compounds of SnSb2Te4 (-Sb2Te3) has the R3 m structure and undergoes a PT towards a C2/m structure (-Sb2Te3). [56] Therefore, the latter phase could be a good candidate for the ternary compound SnSb2Te4 to crystallize in. The same reasoning applies to SnBi2Te4 since -Bi2Te3 also has the R3 m structure and undergoes a PT towards a C2/m structure (-Bi2Te3). [56] Nevertheless, all our attempts to identify the possible HP phase through theoretical simulations failed. Subsequently, we have considered the possibility of a PID. For this purpose, we have calculated the formation enthalpy of SnSb2Te4 in s.g. R3 m and compared it with those of the HP phases of its binary compounds (Figure 5). We have found that above 6.3 GPa the combination of the HP phases -SnTe (s.g. Pnma) and -Sb2Te3 (s.g. C2/m) is energetically more favorable than the LP phase of SnSb2Te4. This result suggests that the ternary compound SnSb2Te4 should decompose into their parent binary materials above 6.3 GPa. In fact, we have found that the ADXRD patterns observed above 7 GPa in SnSb2Te4 (Figure S1) exhibit a perfect fit with the HP phases of the binary parent compounds. A similar theoretical result has been obtained for SnBi2Te4 (see Figure 5), thus suggesting that also PID should be observed in SnBi2Te4 above 7 GPa.

It must be stressed that PID is not a common phenomenon occurring at room temperature, unlike PIA. In fact, similar compounds like Ge2Sb2Te5 undergo PIA at room temperature. [57] The PIA at room temperature is mainly due to the frustration of either a PT to a HP phase or a PID into daughter compounds. [58] This frustration mainly occurs due to kinetic features governed by temperature. In fact, PID is usually observed in complex compounds mostly at high temperature [59][60][61][62] or in some molecular materials, such as H2S, where PID occurs at room temperature and at very HP. [63] SnSb2Te4 is one of the few compounds exhibiting PID at room temperature and relatively LP (7 GPa). This result might be related to the large stability of their polyhedral units that prevail after the PID.

We want to finish by pointing out that the PID of rhombohedral SnSb2Te4 into their binary compounds may explain the superconducting properties recently proposed for this material above 8 GPa, [40] since -Sb2Te3 exhibits a similar superconducting character around the same pressure. [64] Thus,-Sb2Te3 may be responsible for the superconducting properties associated to SnSb2Te4. [65]

Raman scattering measurements under pressure

In order to corroborate the results found in the structural study under pressure, we performed unpolarized HP-RS measurements. Since there is one formula unit (7 atoms) in the primitive unit cell of SnSb2Te4, this compound has twenty-one normal vibrational modes at  with the following mechanical decomposition: [66]  = 3 A1g(R) + 3 A2u(IR) + 3 Eu(IR) + 3 Eg(R) + A2u + Eu where E modes are doubly degenerated, A1g and Eg modes are Raman-active (R) and A2u and Eu are IR-active except for one A2u and one Eu mode that correspond to the three acoustic phonons considering that E-type modes are doubly degenerated. Therefore, there are six Raman-active modes (𝑅𝑎𝑚𝑎𝑛= 3A1g + 3Eg) and six IR-active modes (𝐼𝑅= 3 A2u + 3 Eu). The assignment of the vibrational modes to atomic movements was done through the interface of Jmol Interface for Crystallographic and Electronic Properties (J-ICE) [67] and is discussed in the

SM (see Figures S8 to S17).
Figure S18 shows the unpolarized RS spectrum of SnSb2Te4 at room conditions together with the position of the theoretically predicted frequencies at these conditions (see vertical bottom tick marks). The RS spectrum at room conditions shows five of the six theoretically predicted Raman-active modes. A rather good agreement between the experimental and theoretical Raman-active mode frequencies at room pressure are observed (see also Table S1).

Consequently, we have made a tentative assignment of experimental Raman modes considering the predicted frequencies and pressure coefficients as discussed below.

it is well known that in layered materials vibrational modes at the  point can be classified into interlayer modes (in the low-frequency region) and intralayer modes (in medium-and highfrequency regions). Moreover, layered compounds crystallizing either in rhombohedral, hexagonal or tetragonal space groups, show A (or B) and E modes. In rhombohedral SnSb2Te4, there are two pure interlayer modes (Eg 1 and A1g 1 ), which have the lowest frequencies, and the other ten Raman-and IR-active modes are intralayer modes and have both medium and high frequency values (see Table S1 and Table S2). The two interlayer modes, also known as rigid layer modes, correspond to out-of-phase movements of the neighbor layers both along the a-b plane (Eg 1 mode) and along c-axis (A1g 1 mode).

Figure S18 also shows the unpolarized HP-RS measurements up to 9 GPa. Pressure induces a monotonous shift of the Raman modes towards higher frequencies, except for two modes with negative slope near ambient pressure (see Figure 6). These two modes can be unambiguously assigned to metallic Te [68] and their appearance can be explained by the extreme sensitivity of some selenides and tellurides to visible laser radiation. In fact, Raman modes of trigonal Se and Te with negative slope have been recently identified in HP-RS studies of As2Te3 [47] and HgGa2Se4. [69] The pressure dependence of the experimental and theoretical Raman-active modes in SnSb2Te4 at HP (see Figure 6 and Table S1) shows a good agreement within a 5% accuracy interval. This feature is a clear sign of the good description reached by the ab-initio simulations for this compound. For the sake of completeness, the evolution of the theoretical IR-active modes in SnSb2Te4 is also given in Figure S19 and S20 in SM.

Similar vibrational modes in the low-and high-frequency ranges of SnSb2Te4 are also observed in the parent binary compound -Sb2Te3 (see Figure S21 and Tables S1 andS2). However, there are four vibrational modes of SnSb2Te4 in the medium-frequency region (two Ramanactive and two IR-active) that do not have correspondence on the -Sb2Te3 compound, because they are characteristic of the SL in ternary layered BA2X4 compounds. These extra modes in SnSb2Te4 arise from the vibrations involving the central Sn-Te2 bonds; in particular, out-ofphase vibrations of the Te2 atoms of the SnTe6 polyhedral unit (see Figures S10 andS11).

It is well-known that the rocksalt-type structure of c-SnTe does not have any Raman-active mode but one IR-active mode with T1u symmetry that splits into a doubly degenerate transverse optical (TO) mode and a single longitudinal optical (LO) mode. It is interesting to note that the two extra modes observed in SnSb2Te4 can be related to the two IR-active modes of c-SnTe (see Figure S22). In this context, it can be observed that phonons of similar nature in SnSb2Te4 and -Sb2Te3 are located around similar frequencies (Figure S21), so the position of the two medium-frequency modes in SnSb2Te4 is expected to be located at similar frequencies than in c-SnTe. In particular, there is a clear correlation between the A1g 2 mode of SnSb2Te4 and the LO-type IR-active mode of c-SnTe at room pressure [70] (see Table S2) that is also extended at HP (see Figure S22). Therefore, our Raman results for SnSb2Te4 open a new way to characterize the lattice dynamics of binary compounds with forbidden Raman modes, like those crystallizing in the rocksalt-type structure as c-SnTe, by means of RS measurements in more complex compounds containing similar atomic coordination as those in the binary compounds.

A similar example may be the case of rocksalt-type MgO, whose LO IR-active mode (738 cm -1 ) [71] is consistent with the frequency of the highest Raman-active mode (715 cm -1 ) in MgTiO3 with s.g. R3 . [72] An anomalous decrease of the experimental and theoretical frequency of Raman-active modes A1g 2 and Eg 2 (see Figure 6) and of the theoretical frequency of IR-active modes Eu 2 and Au 2 (see Figure S19) of SnSb2Te4 is observed above 3.0 GPa. The softening of these vibrational modes, mainly related to Sn-Te vibrations could be a priori ascribed to the pressure-induced IPT around 2 GPa, which is similar to that occurring in -Sb2Te3 between 2.5 and 3.5

GPa. [43,73,74] A close look at our theoretical simulations (see Figures S10 andS11) reveal that the Eg 2 and Eu 2 modes in SnSb2Te4 are mainly Sn-Te bending modes with a slight stretching contribution, while the A1g 2 and A2u 2 modes are mainly Sn-Te stretching modes. Since stretching modes mainly depend on the bonding force constant and the bonding distance, the softening of these vibrational modes involving Sn-Te2 bonds could likely be related either to a strong decrease of the Sn-Te2 bonding force constant (depending on the charge density) or to a strong increase of the interatomic distance. However, neither an increase of the Sn-Te2 interatomic distance (Figure S3) nor a decrease of the Sn-Te2 bond charge density (Figure S26) have been observed in the whole studied pressure range. Another possibility to explain the softening is that there is a change of the character of the stretching modes so that they become more bending-like than stretching-like. To prove that, we have looked at the angle between the ab-plane and the Sn-Te2 bond (see Figure S5b). It can be observed that a subtle change in this angle occurs around 4 GPa but the increase of the angle value suggests that these vibrational modes acquire an increasing stretching character, which is incoherent with the loss of bonding strength.

After all these considerations, we have concluded that the softening of the medium-frequency phonons in SnSb2Te4 could only be explained by a Fermi resonance effect. [75] A Fermi resonance occurs when there is a strong anharmonic interaction of a first-order phonon with a two-phonon combination containing a high density of states. In such a case, a frequency shift and a change in the intensity and width of the first-order vibrational mode occurs. The Fermi resonance is a rare phenomenon in solids that has been observed in copper halides, molecules and defect modes. [76][77][78][START_REF] Agranovich | Spectroscopy and Excitation Dynamics of Condensed Moiecular Systems[END_REF] In SnSb2Te4, the sum of the frequencies of the Ag 1 and Eg 1 at  almost coincides in frequency with the Eg 2 mode at 2 GPa; i.e. the pressure range close to the onset of the softening of this mode in SnSb2Te4 (Figure 6). The anomalous softening of the Sn-Te related modes in SnSb2Te4 is also reproduced, even more clearly, by the theoretically predicted evolution of the IR-active LO-mode of c-SnTe at HP (see Figure S22). Note that the frequency of this mode in c-SnTe coincides in frequency at  with twice the value of the TO mode when a sudden change of trend occurs (Figure S22). Therefore, we conclude that c-SnTe exhibits a Fermi resonance in the IR-active LO mode that is also reproduced in the medium-frequency range of SnSb2Te4. This result gives further support to our previous interpretation of the relationship between the vibrational modes of SnSb2Te4 and c-SnTe. In summary, we attribute the softening of Ag 2 and Eg 2 of SnSb2Te4 at HP to a pressure-induced Fermi resonance caused by the coincidence of the frequencies of these firs-order Raman modes and the combination of Ag 1 and Eg 1 modes along the whole BZ.

To close this section, we have calculated the phonon dispersion curves in SnSb2Te4 at 0, 2 and 4 GPa (see Figure S23) in order to understand the nature of the IPT close to 2 GPa previously discussed. As observed, our calculations do not show softening of any of the phonon branches. This result suggests that the pressure-induced IPT found above 2 GPa, cannot be assigned to a 2 nd -order IPT and must be of higher-order. In summary, our analysis of the lattice dynamics of SnSb2Te4 at HP shows the layered character of this compound and a good agreement between our experimental and theoretical data. The Raman-active modes of SnSb2Te4 have been explained in relation to its binary parents -Sb2Te3 and c-SnTe and it has been proved that modes that cannot be observed by Raman scattering in c-SnTe can be observed with this technique in SnSb2Te4 containing similar SnTe6 polyhedra than c-SnTe. Additionally, the anomalous behavior of two Raman-active and two IR-active modes above 3.5 GPa in the medium-frequency region, which are characteristic of the SLs and related to Sn-Te vibrations, has been attributed to a Fermi resonance that also occurs in c-SnTe near 2 GPa. Finally, we have proved, with the help of the phonon dispersion curves for SnSb2Te4 at different pressures, that the IPT occurring in SnSb2Te4 close to 2 GPa is not of 2 ndorder but of higher order, as expected for an IPT of electronic origin.

Electrical resistance measurements under pressure

In the parent binary compound -Sb2Te3, the reported pressure-induced IPT was argued to be associated to a pressure-induced ETT around 3.5 GPa. [43] This result has motivated us to carry out resistance measurements and theoretical calculations of the electronic band structure at different pressures in order to verify if a pressure-induced ETT could be also observed in SnSb2Te4. This kind of measurements have been previously validated by other works [START_REF] Hakeem | [END_REF] up to 50 GPa. Two abrupt variations in the pressure dependence of the electrical resistance of SnSb2Te4 above 2 and 8 GPa have been observed (see Figure 7). The variation above 8 GPa can be ascribed to the PID of the sample, already commented in section A, which is similar to that observed also above 8 GPa in SnBi2Te4. [39] This result confirms our formation enthalpy analysis (Figure 5) that suggest that SnBi2Te4 likely undergoes also a PID. Furthermore, the low resistance measured above 8 GPa can be ascribed to the metallic nature of the HP phases of -Sb2Te3 and c-SnTe. [42,81] Below 8 GPa, we can distinguish two different ranges in the evolution of the electrical resistance of SnSb2Te4 below and above 2 GPa. At the LPs, SnSb2Te4 evidences a very low electrical resistance (constant from room pressure to 2 GPa), whose behavior and values are typical of a degenerate semiconductor. Previous results on the literature [32] have shown that these results correspond to a lack of stoichiometric vacancies, which leads to the formation of a p-type degenerate semiconductor whose carriers are created by cation vacancies. Above 2 GPa, there is a drastic increase of the electrical resistance, which traditionally has been associated in the literature to the creation of structural defects along an ongoing phase transition. [82] These defects might create a donor levels that modify the carrier concentration of the material. In SnSb2Te4, the IPT occurring around 2 GPa might be the responsible for the creation of donor levels associated to defects. These could be able to trap p-carriers, thus helping to pass from a degenerate to a non-degenerate semiconductor or acting as scattering centers that decrease carrier mobility. In any case, the decrease in carrier mobility would be an indication of a decrease of the p-type character of the electrical conduction in SnSb2Te4, similar to that occurs in ZnTe between 7-11 GPa. [82] Thus, the decrease of the conductivity evidenced by SnSb2Te4 above 2 GPa could be exploited to overcome one of the main problems of TIs; i.e. the non-observation of surface carrier conductivity, which would be masked by bulk carrier conductivity. [83] Regarding electronic band structure calculations, we obtain that SnSb2Te4 is an indirect bandgap semiconductor with a bandgap energy Eg= 0.12 eV at room pressure, similar to that previously obtained, [16] and that the bandgap energy decreases with increasing pressure leading to a closening of the bandgap above 4.5 GPa (see Figure S24). Since our calculations based on Density-Functional Theory (DFT) are known to yield underestimated bandgaps when (semi-)local functionals are employed, the value of the real bandgap is expected to be above 0.2 eV at room pressure [11] and the real metallization must occur at higher pressures. In fact, the predicted lack of metallization at LP and the negative slope of the bandgap are compatible with the above-mentioned explanation of the evolution of the electrical resistance at HP. However, we cannot neglect the fact that the lack of hydrostatic conditions above 2.5 GPa due to the use of a solid PTM may blur the interpretations of the changes observed in the electrical properties of the material.

Regarding the possibility of an ETT in SnSb2Te4, our electronic band structure calculations show that the valence band shows no major changes in the whole range of studied pressures; however, there are considerable changes in the conduction band. At 0 GPa, the conduction band minimum is around the  point, but there is a considerable downward shift of the local minimum of the conduction band at the F point with pressure. This minimum becomes the absolute minimum of the conduction band above 4.5 GPa. Therefore, a possible ETT could be expected for n-type material between 0 and 4.5 GPa. Since we work with a p-type material, we cannot attribute the change in resistance near 2 GPa to an ETT.

In summary, our electrical measurements in SnSb2Te4 show a small resistance at LP, typical of a degenerate semiconductor, and an increase of the electrical resistance above 2.0 GPa, attributed to the generation of defects due to the pressure-induced IPT. Finally, the decrease of the electrical resistance above 8 GPa is attributed to the metallic nature of the HP phases of -Sb2Te3 and c-SnTe due to the decomposition of SnSb2Te4 above 7 GPa. The behavior of the electrical resistance in SnSb2Te4 is consistent with our calculations of the electronic band structure that do not show metallization up to 8 GPa when the value of the theoretical bandgap is corrected.

Electronic topology under pressure

Rhombohedral SnSb2Te4 contains different kind of bonds. The vdW interaction between Te1 atoms belonging to different blocks is widely accepted in the scientific community; however, recent studies in chalcogenides have established the difference in the interatomic distance with respect to their vdW radii as an indication that this Te1-Te1 bond is not purely vdW. Thus, the assignation to this separation as vdW gap would be reinterpreted as vdW-like gap. [37,84] The nature of the bonds between Sn-Te2, Sb-Te2 and Sb-Te1 are also the focus of intense debates. According to the Lewis' octet rule, the Sb 3+ and Sn 2+ cations bonds to Te 2-should not have the octahedral coordination observed here, and this has been explained in the literature by delocalization of the charge by means of a chalcogen or hypervalent interaction. [85,86] In our case, the bonds are not established among chalcogen atoms, but between a chalcogen anion and different kind of cations. This scenario may imply that we can neglect the chalcogen bonding as responsible for the interactions above-mentioned. On the other hand, the concept of hypervalency has been extensively studied and is a subject of strong discussions up to date. The most recent and accepted quantitative approximation to this concept was performed by Durrant, [87] where the valence equivalent electron parameter defined by "the formal shared electron count at a given atom, obtained by any combination of valid and covalent resonant form". This parameter discerns between molecules that can be considered as hypervalent or obeying a "modified octet rule". For instance, XeF2 molecule [88] should obey a modified octet rule, the same as occurs for our SbTe6 and SnTe6 polyhedral units. The bond character for the XeF2 molecule has been explained by the concept of a charge-shift bond, which is usually established between a central atom with low ionization potential and a strongly electronegative ligand. In our case, the SbTe6 or SnTe6 polyhedral units are described without significant difference between their electronegativities. The unfortunate attempt to describe the chemical interactions involved on these polyhedral units led us to explore new kind of bonds. Thus, the interactions in both parent binary compounds of SnSb2Te4 (-Sb2Te3 and c-SnTe) have been recently explained by the so-called metavalent bonding, [34][35][36][37] where electrons are shared between nearest neighbors without electron transfer allowing to exceed the octet rule limitation. The use of this denomination is still under controversy, because some authors claimed that the bonding in chalcogenides can be explained by molecular-orbital approach or valence-bond theory of hyperbonding, [89] where that hypervalence bonding is a special case of charge-shift bonding. [90]

Bader charge analysis

In recent HP works of -Sb2Te3, the occurrence of a pressure-induced IPT was studied on the light of the electron density evolution under pressure. [74] Additionally, the pressure-induced ETT was interpreted on the light of the evolution of the Bader charges at HP. [73] Since the occurrence of a pressure-induced ETT depends on the location of the Fermi level, it is rather doubtful that the pressure at which an ETT is observed can be determined with the study of the theoretical Bader charge analysis, which is independent of the location of the Fermi level.

However, a change in the evolution of the Bader charges at HP can be indicative of a pressureinduced IPT, not related with a variation of the Fermi level.

Figure 8a shows the pressure dependence of the Bader charges for each of the constituent atoms of SnSb2Te4. The Bader charges of the internal atoms of the SLs (Sn and Te2 atoms), related to the SnTe6 polyhedral units, are larger than those of the external atoms of the SL (Sb and Te1) related to the SbTe6 polyhedral units, and describe a monotonous trend with respect to pressure following an almost linear behavior with a small kink near 2 GPa. On the other hand, the pressure evolution of the Bader charges of the most external atoms of the SLs cannot be fitted to a single linear trend and two linear fits below and above 2 GPa are required.

The comparison between the polyhedral net charges contained in the two octahedral units that compose this ternary material (Figure 8b) reveals a clear change of trend above 2 GPa (Figure 8c). An abrupt charge transfer from SbTe6 towards SnTe6 occurs up to 2 GPa and ceases above this pressure. This evolution can be explained as follows: At LP, the closening of the inter-layer gap leads to a strong charge redistribution of the external SbTe6 unit that lead to a charge transfer to the SnTe6 unit. Above 2 GPa, the vdW-like space is already closed and no further charge is transferred between both SnTe6 and SbTe6 units so their Bader charges evolve similarly under pressure. In summary, the charge redistribution between the polyhedral units is consistent with Te1 atoms being involved in the SbTe6 octahedral units and being the ones responsible for the vdW interactions in the inter-layer gap that define the IPT around 2 GPa in SnSb2Te4.

Non-Covalent Interaction analysis

We have performed Non-Covalent Interaction (NCI) simulations [91,92] to probe the evolution of the low electron density regions at the inter-layer space between two neighbouring SLs. Figure S25 in SM highlight the vdW-like interactions at the inter-layer (Te1-Te1) space at LP and their evolution towards more localized interactions at HP. A 2D data profile of the NCI of the interlayer space between two SLs is represented in Figure 9. This figure can be interpreted as follows: At LP, the electron density cloud is very flat and delocalized but the fact that the interatomic distance is smaller than the vdW diameter might imply a certain localized character, even if the vdW bond is predominant. Above 2 GPa, bonds become more localized; thus, clear bonds appear among polyhedra of neighbor SLs. Overall, all results point at charge localization with increasing pressure so that the Te1-Te1 vdW nature of the inter-layer space is no longer governing the response of the solid above 2 GPa.

Electronic density analysis

A more quantitative analysis of the electronic topology can be done by analyzing the evolution of two parameters, such as the electron charge density, 𝜌(𝑟 ⃗), and its Laplacian, ∇ 𝜌(𝑟 ⃗), at the bond critical point (BCP), which can be defined by the point of minimum electron density between two bonded atoms (following the electron density gradient). This method allows us to determine the bonding character of the four bounds found in SnSb2Te4 (Te1-Te1, Sb-Te1, Sb-Te2 and Sn-Te2).

With regards to the Te1-Te1 interaction, we can distinguish its predominant vdW character at LPs, determined by a low 𝜌(𝑟 ⃗) and a positive value of the ∇ 𝜌(𝑟 ⃗) at the BCP (see Figure S26).

However, these values are higher than those found in vdW complexes. [93] Then, we cannot neglect that the interlayer interaction may be influenced by a certain charge transfer caused by the Sb-Te1 bond, as suggested by Cheng et al. [37] An increase of both parameters at HP is coherent with the decrease of vdW character [94] we have already observed and commented in the previous section. At LP, Te1 atoms are bonded to three Sb atoms and at close vicinity with other three Te1 atoms, belonging to the neighboring layer, at much larger distance. At HP, the strong decrease of the interlayer Te1-Te1 distance gives rise to a stronger interaction between the Te atoms belonging to different layers, thus leading to a sixfold coordination of the Te1 atoms. This Te1-Te1 interaction supports the evidence of the formation of more ionic bonds between the neighboring Te atoms since ionic bonds are characterized by large and positive 𝜌(𝑟 ⃗) and positive ∇ 𝜌(𝑟 ⃗) at the BCP (see Table S3).

With respect to the Sb-Te2 and Sn-Te2 bonds, they possess similar values of 𝜌(𝑟 ⃗) and ∇ 𝜌(𝑟 ⃗) at the BCP in the whole pressure range studied. In fact, the value of 𝜌(𝑟 ⃗) for both bonds is intermediate between that of Sb-Te1 bond and the weak vdW interaction between Te1 atoms along the whole of the studied pressure range. In this context, we have to recall that both parent binary compounds, -Sb2Te3 and c-SnTe, have been considered as incipient metals, [34][35][36][37] therefore these values of 𝜌(𝑟 ⃗) and ∇ 𝜌(𝑟 ⃗) could be characteristic parameters of metavalent bonding with partially delocalized electrons.

Regarding the Sb-Te1 bond, it evidences a very high 𝜌(𝑟 ⃗) when compared to the overall interactions and a positive, although close to zero, value of the ∇ 𝜌(𝑟 ⃗) at the BCP in the whole pressure range studied. The high 𝜌(𝑟 ⃗) value is typical of covalent or ionic bondings; however, the ∇ 𝜌(𝑟 ⃗) value must be negative (positive) for a covalent (ionic) bonding. Therefore, the small positive ∇ 𝜌(𝑟 ⃗) value suggests a mixture between the covalent and metavalent bonding.

Note that a polar covalent interaction is neglected because typically it should show a value of ∇ 𝜌(𝑟 ⃗) closer to zero. Sb-Te2 and the Sn-Te2 bonds may fall into what has been recently defined to be the metavalenttype bonding. Finally, we have fully characterized all the bond types present in SnSb2Te4 by analyzing the electron density. Thus, we have proposed a new method (by using the concepts of 𝜌(𝑟 ⃗) and ∇ 𝜌(𝑟 ⃗) at the BCP) to identify the bond character in complex structures, where a coexistence of several types of interactions occurs.

Conclusion

Our study of the compressed rhombohedral phase of SnSb2Te4 at room temperature shows that the rhombohedral phase is stable up to 7 GPa and that a decomposition of the sample occurs above this pressure. This behavior has been framed within the orbital radii map of the telluriumbased ternary chalcogenides (that has been extended) and a possible path at HP has been described for SnSb2Te4 that can be useful to understand other isostructural compounds of the BA2Te4 family.

The compressed rhombohedral structure of SnSb2Te4 shows an isostructural phase transition above 2 GPa that is mainly caused by a change in the compressibility of the inter-layer space, governed mostly by vdW interactions between the external Te atoms of the SLs, which also dominate the behavior of the unit-cell volume under compression. The change in the compressibility of the inter-layer space is clearly reflected on the analysis of the pressure dependence of the calculated electron density topology.

The study of the lattice dynamics of SnSb2Te4 under compression has allowed us to understand the atomic vibrations of the different phonons and assign the mode symmetries of the Ramanactive modes. Furthermore, the description of the atomic vibrations has been compared with their parent binary compounds (c-SnTe and -Sb2Te3). A softening of vibrational modes mainly related to the Sn-Te bonds occurs above 3 GPa, and such a feature has been explained within the framework of the Fermi resonance. Our calculations predict that the Fermi resonance must also be observed in the HP dependence of IR-active modes of parent binary c-SnTe around 2 GPa. Our results show strong correlation between the vibrational modes of SnSb2Te4 and those of its parent binary compounds. In fact, the Raman spectrum of SnSb2Te4 shows vibrational modes that are forbidden in c-SnTe; thus showing a novel way to experimentally observe the forbidden vibrational modes of some compounds.

We have also undertaken a study of the pressure dependence of the electrical properties of SnSb2Te4 with unintentionally p-type semiconducting character in order to verify if an ETT could be observed. The change in the electrical resistance above 8 GPa has been attributed to the sample decomposition; however, a drastic increase in resistance was observed above 2 GPa. This increase has not been attributed to an ETT due to the p-type character of our sample, but to the generation of defects on the ongoing IPT passing from a p-type degenerate to a nondegenerate semiconductor by the reduction of the hole carrier concentration. This result allows the tuning of the electrical properties to improve the TI capabilities of this compound.

Finally, our electron density topology analysis shows that the IPT around 2 GPa is related to the loss of the predominant vdW character by an increment of the ionic character of the interaction between the Te1 atoms of neighbor SLs, so the hardening of the Te1-Te1 bond may be the cause of the IPT. The lack of soft phonon branches along the Brillouin zone confirms that the observed IPT is related to a phase transition of higher order than 2; i.e. it is an IPT of electronic origin.

The analysis of the ELF of the Sb-Te1 interaction displays a polar covalent bond character, which remains unalterable under compression. However, the most interesting analysis is obtained when studying the ELF along the Sb-Te2 and Sn-Te interactions, which show the typical intermediate values expected for metavalent bonding. The evaluation of their electronic densities and respective Laplacians at the BCP provides a new criterion to identify these interactions when the material is very complex and different kinds of bonds coexist.

In summary, our study provides new insights into the physics and chemistry of ternary topological insulators of the tetradymite-like ternary BA2X4 materials and highlights the importance of the study of the evolution of the chemical bonds under pressure of topological insulators in order to understand the origin of isostructural phase transitions observed in this family of compounds and the possibility to tune their exceptional properties in a better way than in binary topological insulators.

Experimental Section

Sample preparation: Bulk samples were prepared by melting stoichiometric amounts of the pure elements Sn (99.999%, Smart Elements), Sb (99.999%, Smart Elements) and Te (99.999%, Alfa Aesar) at 950 ºC for 93h in sealed silica glass ampoules under argon atmosphere and subsequent annealing at 450 -500 °C for two days. [31] Representative parts of the samples were crushed to powders and fixed on Mylar foils with silicon grease to collect powder diffraction patterns on a Huber G670 powder diffractometer equipped with an imaging plate detector (Cu-K1 radiation, Ge monochromator,  = 1.54051 Å) in Guinier geometry. Rietveld refinement of powder x-ray diffraction data confirmed the high purity of the samples.

Theoretical Calculations: Ab-initio calculations have been performed within the density functional theory (DFT) [97] using plane-wave basis-sets and the projector-augmented wave (PAW) [98] scheme with the Vienna Ab-initio Simulation Package (VASP) package. [99] Calculations of the electronic-band structures have been considered by employing spin-orbit coupling (SOC). The plane-wave kinetic-energy cutoff was defined with 320 eV, in order to achieve highly converged results. We have used the generalized-gradient approximation (GGA) for the exchange-correlation energy with the Perdew-Burke-Ernzerhof parameterization revised for solids (PBEsol). [100] At each selected volume, the structures were fully relaxed to their equilibrium configuration through the calculation of the forces on atoms and the stress tensor with a dense special k-point sampling Monkhorst-Pack grids. In particular, the electronic band structures along high-symmetry directions and the corresponding electronic density of states (EDOS) were computed with a mesh of 18x18x18 k-points. The application of DFT-based calculations to the study of semiconductor properties under HP has been reviewed in the literature. [101] Lattice-dynamics calculations of phonon modes were performed at the zone center ( point) of the Brillouin zone. For the calculation of the dynamical matrix at  we used the direct force-constant approach (or supercell method), [99,102] which involves the calculation of all the atomic forces when each non-symmetry related atom in the unit cell is displaced along nonsymmetry related directions.

The Bader analysis was performed by partitioning the PBEsol-DFT core and valance charge density grids. [103][104][105][106][107] A fine FFT grid was required to accurately reproduce the correct total core charge. The Non-Covalent Interactions (NCI) of the PBEsol-DFT charge densities was computed using the NCIPLOT tool. [91,92] Such a tool defines a visualization index based on the electron density and its derivatives, enabling identification of non-covalent interactions, based on the peaks that appear in the reduced density gradient at low densities.

Synchrotron based angle-dispersive X-ray diffraction (ADXRD) under pressure experiments:

HP-ADXRD measurements on SnSb2Te4 at 300 K using a membrane-type diamond-anvil cell (DAC) were carried out in experiment 1 (experiment 2) up to 37 GPa (12 GPa) in beamline I15 (MSPD beamline [108] ) at Diamond Light Source synchrotron (ALBA synchrotron) using a monochromatic X-ray beam with λ = 0.42408 Å (λ = 0.4246 Å). In experiment 1 (experiment 2) images were collected using a MAR345 image plate (Rayonix MARCCD detector) located at 430 mm (240 mm) from the sample. In experiment 1 (experiment 2), SnSb2Te4 powder was loaded in a 150-μm diameter hole of a Rhenium (Inconel) gasket in a DAC with diamondculet sizes of 350 μm using helium (silicone oil) as pressure transmitting medium (PTM). In both experiments, copper was placed inside the pressure cavity and used as the pressure sensor through copper EoS [109] and a pinhole placed before the sample position was used as a clean-up aperture for filtering out the tail of the X-ray beam, which was focused down to 20 x 20 μm 2 using Kickpatrick-Baez mirrors.

Diffraction patterns obtained in both experiments were integrated as a function of 2θ using FIT2D software in order to give conventional, one-dimensional diffraction profiles. [110] The refinement of the powder diffraction patterns was performed using GSAS program package. [111,112] Due to the resonant excitation energy with Sn K-edge used in both experiments, the relative intensities are not accurate enough to perform Rietveld refinement but a Von Dreele-type Le Bail fit. Therefore, all the experimental structural parameters presented in this work have been obtained by means of a Von Dreele-type Le Bail method.

Unfortunately, the lack of Rietveld refinement in our measurements prevents us from validating the degree of cation mixing in our samples.

Raman scattering (RS) measurements under pressure: Unpolarized HP-RS measurements up to 27 GPa using a membrane-type DAC and 16:3:1 methanol/ethanol/water mixture as PTM (quasi-hydrostatic up to 10 GPa), [113,114] were performed with a Horiba Jobin Yvon LabRAM UV HR microspectrometer equipped with a thermoelectrically cooled multichannel charge coupled device detector which allows a spectral resolution better than 2 cm -1 . The Raman signal was excited with a He-Ne laser (632.8 nm line) with a power of less than 10 mW and collected in backscattering geometry using an edge filter working in perpendicular configuration and cutting at 100 cm -1 . Raman signals down to 50 cm -1 can eventually be detected by adjusting the angle between the edge filter and the light containing the Raman signal (provided that the Rayleigh signal is weak enough and the Raman signal is strong enough). Pressure was determined by the ruby luminescence method. The frequency of the Raman-active phonons has been experimentally analyzed by fitting Raman peaks with a Voigt profile fixing the Gaussian line width (1.6 cm -1 ) to the experimental setup resolution. [117,118] Transport properties under pressure: Electrical resistance of SnSb2Te4 under pressure was measured with the standard four-point probe van der Pauw method using 20 µm copper-beryllium wires. Single crystals of SnSb2Te4 of approx. 30 µm thick and 100 x 100 µm 2 surface were loaded into a Merrill-Bassett DAC with 400 µm culet diamonds. The electrical average resistance was measured by using four 20 µm copper-beryllium wires. Electrical resistance was measured under two different arrangements. In the first one, the sample was directly in contact with the anvils; i.e. under non-hydrostatic conditions. In the second one, the sample was inside a stainless steel gasket and surrounded by CsI powder as PTM; i.e. under quasi-hydrostatic conditions. Electrical resistance showed similar trends in both arrangements, likely due to the anisotropic (layered) and soft nature of the crystals.

Luminescence lines of Ruby powder were used to calibrate the pressure inside the cavity in both methods. [115,116] The inset shows the evolution of the c/a ratio with pressure. Solid lines represent the theoretically simulated data, dashed lines represents the fit to EoS equations, solid circles are the experimental data obtained using silicone oil as PTM and solid squares are the experimental data obtained using helium as PTM.

Pressure (GPa)

0 1 2 3 4 5 6 7
Lattice parameter (Å) Quadratic Elongation (AX 6 ) Pressure dependence of the experimental (symbols) and theoretical (lines) Raman-active mode frequencies in SnSb2Te4. Dotted line represents the pressure dependence of the A1g 1 + Eg 1 combination at , while dashed lines represent the Raman-active modes expected for -Sb2Te3.

Pressure (GPa) Table 2. Calculated (th.) and experimental (exp.) bulk modulus (B0) of the lattice parameters of SnBi2Te4 and SnSb2Te4 and their associated axial compressibilities.

Table 3. Theoretical and experimental Raman-active mode frequencies and their pressure coefficients of SnSb2Te4 at room temperature as fitted with equation P = 0 + aP + bP 2 compared with those of theoretically simulated -Sb2Te3. Mode symmetry SnSb2Te4 and in -Sb2Te3 [S6] and cubic SnTe. [S8] Pressure (GPa) Angle between bond and a-b plane (degree)

0 (cm -1 ) a (cm -1 /GPa) b (cm -1 /GPa 2 ) 0 (cm -1 ) a (cm -1 /GPa) b (cm -1 /GPa 2 ) 0 (cm -1 ) a (cm -1 /GPa) b (cm -1 /GPa 2
36.9 A first comparison can be stablished between the vibrational modes at  in SnSb2Te4 and the parent compound Sb2Te3. In Sb2Te3 there are four Raman-active modes (Eg 1 , A1g 1 , Eg 2 and A1g 2 ) and four IR-active modes (Eu 1 , Eu 2 , A2u 1 and A2u 2 ) and referenced in order of increasing frequency [S5,S6]. As regards to the Raman-active modes, the interlayer modes of -Sb2Te3 are the Eg 1 and A1g 1 modes (Figure S14) and these are similar to the Eg 1 and Ag 1 modes of SnSb2Te4 (Figure S8). For all these modes the central part of the layer remains almost static and the external adjacent Sb and Te atoms in a sublayer vibrate in-phase and also out-of-phase with respect to the atoms of the other adjacent sublayer. Similarly, the intralayer Eg 2 and A1g 2 modes of Sb2Te3 (Figure S15) are similar to the intralayer Eg 3 and Ag 3 modes of SnSb2Te4 (Figure S13) since for all these modes the central part of the layer remains almost static and the external adjacent Sb and Te atoms in a sublayer vibrate, among them and with respect to atoms of the other sublayer, out-of-phase. The similarity of Eg 2 and A1g 2 modes in Sb2Te3 and Eg 3 and Ag 3 modes in SnSb2Te4 is so remarkable that these modes possess practically the same theoretically predicted frequency values (see Table S1). With respect to the Raman-active Eg 2 and Ag 2 modes of SnSb2Te4 (Figure S11), these have no analog on -Sb2Te3 since both modes involve out-of-phase vibrations of the internal Te atoms, which cannot occur in Sb2Te3 with only one internal Te atom. Finally, it is noteworthy of mentioning that the IR-active Eu 1 and Au 1 modes of SnSb2Te4 have no resemblance with IR-active modes in Sb2Te3. Note that these two modes refer to the Sb atoms vibrating in-phase with their adjacent external Te atoms, a feature that does not occur in any of the IR-active modes of Sb2Te3. Finally, it must be stressed that for all IR-active modes of -Sb2Te3, Sb atoms of the two sublayers vibrate in-phase, while for all Ramanactive modes of -Sb2Te3 vibrate out-of-phase. The same behavior is observed in SnSb2Te4. This is the main characteristic to discern between Raman-active and IR-active modes of both compounds. Referring to the pressure coefficients of the different Raman-active and IR-active modes, it can be observed that generally the A modes have larger pressure coefficients than their associated E modes, as it is expected in non-polar layered compounds with van der Waals forces between their layers (see Tables S1 andS2). This has been already commented for interlayer Raman-active Eg 1 and A2g 1 modes and it applies to both SnSb2Te4 and Sb2Te3.

Usually, the small pressure coefficient of the low-frequency E mode in layered materials is ascribed to the weak bending force constant due to weak van der Waals forces between the neighboring layers. On the other hand, the large pressure coefficient of the low-frequency A mode is due to the extraordinary increase of the stretching force constant between neighboring layers due to the strong decrease of the interlayer distance. [S4,S7] This behavior is also found for the low-frequency interlayer modes in layered Sb2Te3 and SnSb2Te4, and it is also valid for the other pairs of intralayer E and A modes, previously commented. This can be understood if intralayer E modes are mainly associated to bending Sb-Te (Sb-Te and Sn-Te) modes in Sb2Te3 (SnSb2Te4), while intralayer A modes are mainly associated to stretching Sb-Te (Sb-Te and Sn-Te) modes in Sb2Te3 (SnSb2Te4). This reasoning allows also to explain the reason for which the A modes always possess larger frequencies than their associated E modes. The most notable deviation of the rule mentioned above of the Raman-active modes, is that of the Eg 3 mode in SnSb2Te4. The theoretical pressure coefficient of this mode is larger than its associated A2g 3 mode. This feature contrasts with Sb2Te3 where the equivalent modes Eg 2 and A2g 2 show a normal behavior. Additionally, it must be noted that the pressure coefficient at zero pressure obtained for the A2g 2 mode in SnSb2Te4 is quite high because the fit has been performed with high-pressure data due to the lack of values near room pressure.

The larger pressure coefficient of the A modes when compared to their corresponding E modes also applies for IR-active modes. Note that in Sb2Te3 the pressure coefficient of Eu 1 mode is smaller than its associated A2u 2 mode and that of the Eu 2 mode is smaller than its associated A2u 1 mode. This reasoning also applies to their similar IR-active modes in SnSb2Te4; i.e., the Eu 2 and A2u 2 and the Eu 3 and A2u 3 modes, respectively. Moreover, the same Table S2. Frequencies and pressure coefficients at zero pressure of the theoretical IR-active modes in SnSb2Te4, Sb2Te3 and SnTe. Spin-orbit coupling has been included in all theoretical calculations.

Table S3. Values of the electronic charge density and its gradient at the BCP as well as the ELF along different types of bondings.

Figure 1 .

 1 Figure 1. 3D structure layout of the SnSb2Te4 compound. Atomic planes are defined.

Figure 2 .

 2 Figure 2. Pressure dependence of the unit cell volume (a) and lattice parameters (b).The inset shows the evolution of the c/a ratio with pressure. Solid lines represent the theoretically simulated data, dashed lines represents the fit to EoS equations, solid circles are the experimental data obtained using silicone oil as PTM and solid squares are the experimental data obtained using helium as PTM.

Figure 3 .

 3 Figure 3. Relationship between the quadratic elongation of the BX6 octahedron and the quadratic elongation of the AX6 octahedron in AB2X4 materials. Structures obtained from Refs.[27,28,119-122]

Figure 4 . 4 Figure 5 .

 445 Figure 4. Updated orbital radii map of stable BA2Te4 compounds initially proposed by Zhang et al. [54]

1 Figure 7 .Figure 8 .Figure 9 .

 1789 Figure 7. Evolution of the resistance of compressed SnSb2Te4 recorded during the upstroke.

Figure 10 .

 10 Figure 10. Pressure dependence of the ELF along the path of the Sb-Te1, Sb-Te2, Sn-Te and Te-Te bonds at 0 GPa (a) and 6.8 GPa (b).

  a) This work Title ((no stars)) ToC figure ((Please choose one size: 55 mm broad × 50 mm high or 110 mm broad × 20 mm high. Please do not use any other dimensions))

Figure S2 .

 S2 Figure S2. Pressure dependence of the theoretical volumes of SbTe6 and SnTe6 octahedra in

Figure S3 .Figure S5 .

 S3S5 Figure S3. Pressure dependence of the theoretical interatomic distances in SnSb2Te4 (circles)

Figure S6 . 6

 S66 Figure S6. Pressure dependence of the theoretical quadratic elongation in the SbTe6 and

Figure S8 .

 S8 Figure S8. Atomic movements (see arrows) of low-frequency interlayer Raman-active modes

Figure S9 .

 S9 Figure S9. Atomic movements of IR-active modes Eu 1 (left) and A2u 1 (right) located near 62

Figure S10 .

 S10 Figure S10. Atomic movements of IR-active mode Eu 2 (left) and A2u 2 (right) located near 65

Figure S11 .

 S11 Figure S11. Atomic movements of middle-frequency Raman-active modes Eg 2 (left) and A1g 2

Figure S12 .

 S12 Figure S12. Atomic movements of IR-active modes Eu 3 (left) and Au 3 (right) located near 112

Figure S13 .

 S13 Figure S13. Atomic movements of Raman-active modes Eg 3 and Ag 3 located near 117 and

Figure S14 .

 S14 Figure S14. Atomic movements (see arrows) of low-frequency interlayer Raman-active

Figure S15 .

 S15 Figure S15. Atomic movements (see arrows) of high-frequency intralayer Raman-active

Figure S16 .

 S16 Figure S16. Atomic movements (see arrows) of intralayer IR-active modes Eu 1 and A2u 2 in

Figure S17 .

 S17 Figure S17. Atomic movements (see arrows) of intralayer IR-active modes Eu 2 and A2u 1 in

Figure S18 .

 S18 Figure S18. Raman scattering spectra of rhombohedral SnSb2Te4 at different pressures up to

Figure S19 . 3 Figure S20 . 3 Figure S21 .

 S193S203S21 Figure S19. Pressure dependence of the theoretical IR-active modes of SnSb2Te4. A modes

3 Figure S22 .Figure S23 .

 3S22S23 Figure S22. Pressure dependence of the experimental (symbols) and theoretical (lines)

FrequencyFigure S25 .

 S25 Figure S25. Reduced density gradient map of rhombohedral SnSb2Te4 around the interlayer

Figure S26 .

 S26 Figure S26. Pressure dependence of the electron density (left) and Laplacian of the electron

Table 1 .

 1 Calculated (th.) and experimental (exp.) Volume (V0), bulk modulus (B0), and its derivative (B0') of SnBi2Te4 and SnSb2Te4 at ambient pressure. Calculations including SOC in this work; c) Average experimental value from Ref.43; d) Calculations including SOC from Ref.43.

		V0 (Å 3 )	B0 (GPa)	B0'
		SnSb2Te4
	exp. a	663.1(6)	31.6(14)	8(8)
	th.(GGA-PBESol) b	659.3(6)	41.0(15)	6.5(6)
		-Sb2Te3
	exp. c	481.1(8)	36.1(9)	6.2(4)
	th.(GGA-PBESol) d	473.1(8)	43(2)	4.3(5)
	a) This work; b)

  )

	Eg 1	-	-	-	38.87(15)	2.52(8)	-0.081(9)	50.4	2.62	-0.09
	A2g 1	53.3(8)	4.2(6)	-0.15(8)	55.3(2)	4.25(12)	-0.145(12)	68.9	4.3	-0.07
	Eg 2	103.3(4)	3.7(7)	-0.4(2)	100.51(8)	2.45(6)	-	116.6	2.11
	A2g 2	107.8(14)	4.6(6)	-0.15(6)	115.1(2)	2.70(18)	-	167.6	2.57
	Eg 3	-	-	-	116.65(17) 4.63(13)	-
	A2g 3	160.87(14) 2.68(11)	-0.035(15)	167.10(16)	3.38(8)	-0.041(9)

Acknowledgements

This work has been performed under financial support from Spanish MINECO under projects MALTA Consolider Ingenio 2010 network (MAT2015-71070-REDC) and projects FIS2017-83295-P and MAT2016-75586-C4-1/2/3-P, from Generalitat Valenciana under project PROMETEO/2018/123. This publication is fruit of "Programa de Valoración y Recursos Conjuntos de I+D+i VLC/CAMPUS and has been financed by the Spanish Ministerio de Educación, Cultura y Deporte as part of "Programa Campus de Excelencia Internacional". Supercomputer time has been provided by the Red Española de Supercomputación (RES) and the MALTA cluster. JAS acknowledges "Ramón y Cajal" fellowship (RYC-2015-17482) program for financial support and ELdS acknowledges Marie Sklodowska-Curie grant No. 785789-COMEX from European Union's Horizon 2020 research and innovation programme. We also thank ALBA synchrotron and DIAMOND light source for funded experiments.

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In order to deepen into the analysis of the character of these two bonds, we have plotted the ELF along the different atomic interaction distances of SnSb2Te4; namely, Te1-Te1, Sb-Te1, Sb-Te2 and Sn-Te2 (see Figure 10 and Figure S27). ELF describes the character of bond formation between the involved atoms. At LPs, the low ELF values (close to 0.2) close to the center of the Te1-Te1 distance, exhibit the typical values of vdW bonds; however, this ELF signal increases rapidly with pressure towards values characteristic of an ionic-type bond in good agreement with the results observed from the BCP electronic topological analysis. In the case of the Sb-Te1 bond, the ELF value close to the center of its respective interatomic distance is high enough (0.7) to ensure we are dealing with a strong bond, coherent with the polarcovalent results previously obtained from the BCP analysis.

Regarding the ELF signals between the Sn-Te and the Sb-Te2 bonds, these have a medium value (0.5-0.6), which is close to the center of the interatomic distance. This value has been associated in the literature to be of metavalent bonding character. [34,35,95,96] The intermediate values of 𝜌(𝑟 ⃗) of both bonds, at the BCP and ELF, can be explained by the partial delocalization of electrons of this type of bonding, which stems from the sharing of electrons between several bonds; i.e. there is one single electron per bond instead of two in a typical covalent bond. Therefore, our ELF values support the previous analysis of 𝜌(𝑟 ⃗) and ∇ 𝜌(𝑟 ⃗) at the BCP for both interactions. In this way, we have established a new form of identifying metavalent bonds;

i.e. they are characterized by an intermediate value of 𝜌(𝑟 ⃗) and a low positive value of ∇ ⃗ 𝜌(𝑟 ⃗).

The classification of the different bondings according to 𝜌(𝑟 ⃗), ∇ 𝜌(𝑟 ⃗) and ELF are summarized in Table S3 in SM.

In summary, we conclude that the changes observed both at the Bader and NCI analyses reflect the IPT occurring from the rhombohedral SnSb2Te4 close to 2 GPa. This IPT is strongly related to the hardening of the Te1-Te1 interlayer interaction and the loss of their predominant vdW character. Moreover, we have shown that Sb-Te1 bonds are polar covalent bonds, whereas the Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

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Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2018.

Supporting Information

Supplementary Information of "Characterization and decomposition of the natural van der Waals SnSb2Te4 under compression" Juan Ángel Sans,* Rosario Vilaplana, Estelina Lora Da Silva, Catalin Popescu, Vanesa Paula Cuenca-Gotor, Adrián Andrada-Chacón, Javier Sánchez-Benitez, Oscar Gomis, André Luis de Jesus Pereira, Plácida Rodríguez-Hernández, Alfonso Muñoz, Dominik Daisenberger, Braulio García-Domene, Alfredo Segura, Daniel Errandonea, Ravhi Kumar, Oliver Oeckler, Philipp Urban, Julia Contreras-García, and Francisco J. Manjón

Structural features of SnSb2Te4

In SnSb2Te4, roughly 50% of Sb cations are mixed with Sn cations in the 3a Wyckoff site and 25% of Sn are mixed with Sb cations in 6c atomic position. This result will not affect to the interlayer character featured by van der Waals interactions between Te sublayers. The similar covalent radii of Sn and Sb (1.39 Å in both) [S1] and ionic radii in an octahedral distribution, with a value of 83 Å for Sn and 90 Å for Sb [S2] suggests that the perturbation in the Sb-Te and Sn-Te octahedral units will be mostly influence by the electronic interactions, instead of geometrical effects. On the other hand, the isostructural SnBi2Te4 shows a similar mixed cationic occupancy as its counterpart SnSb2Te4. According to Kuropatawa and Kleinke, [S3] Sn remains mostly on the 3a atomic position with an occupancy of 74% like Bi that is in 6c atomic position with an occupancy of 68%.