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Polytypism, polymorphism and superconductivity in TaSe2-xTex

Polymorphism in materials often leads to significantly different physical properties - the rutile and anatase polymorphs of TiO2 are a prime example. Polytypism is a special type of polymorphism, occurring in layered materials when the geometry of a repeating structural layer is maintained but the layer stacking sequence of the overall crystal structure can be varied; SiC is an example of a material with many polytypes. Although polymorphs can have radically different physical properties, it is much rarer for polytypism to impact physical properties in a dramatic fashion. Here we study the effects of polytypism and polymorphism on the superconductivity of TaSe2, one of the archetypal members of the large family of layered dichalcogenides. We show that it is possible to access 2 stable polytypes and 2 stable polymorphs in the TaSe2-xTex solid solution, and find that the 3R polytype shows a superconducting transition temperature that is nearly 17 times higher than that of the much more commonly found 2H polytype. The reason for this dramatic change is not apparent, but we propose that it arises either from a remarkable dependence of Tc on subtle differences in the characteristics of the single layers present, or from a surprising effect of the layer stacking sequence on electronic properties that instead are expected to be dominated by the properties of a single layer in materials of this kind.

Structurally, these compounds can be regarded as having strongly bonded (2D) X-M-X layers, with M in either trigonal prismatic or octahedral coordination with X, and weak inter-layer X-X bonding of the van der Waals type. Many of these materials manifest charge density waves and the competition between CDWs and superconductivity, e.g. (5)(6)(7)(8)(9). Among the TMDCs, the 2H polytype of tantalum diselenide (2H-TaSe 2 ) is considered one of the foundational materials (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), showing a transition from a metallic phase to an incommensurate charge-density-wave (ICDW) phase at 123 K, followed by a "lock-in" transition to a commensurate charge-densitywave (CCDW) phase at 90 K. It finally becomes a superconductor with a rather low T c of 0.15 K. Although detailed studies have been performed on the physics of CDWs and superconductivity in 2H-TaSe 2 (16)(17)(18), a comparative study of the superconductivity of the polytypes and polymorphs of TaSe 2 from the chemical perspective has not been done. TaSe 2 is highly polymorphic, possibly the most polymorphic of the TMDCs (19). In some of its forms, notably the 2H and 3R polytypes (Figure 1a), Ta is found in trigonal prismatic coordination in Se-Ta-Se layers that are stacked along the c axis of the hexagonal (or rhombohedral) cell. The 2H and 3R polytypes differ only in their stacking periodicitythe structure repeats after 2 layers in the 2H form and 3 layers in the 3R form (20)(21)(22). The 3R form can be synthesized, but it is not the stable variant (the 2H form is) and so has been the subject of little study. In one of the other polymorphs, the 1T type, Ta is found in octahedral coordination in the Se-Ta-Se layers, and the layer stacking along the c axis of the trigonal cell such that the structure repeats after only one layer (23) (Figure 1a). Again, the 1T form has not been the subject of much study. Here we show that the 3R and 1T polymorphs are both quite stable in the TaSe 2-x Te x system, and that they are both superconducting.
For pure TaTe 2 , the monoclinic structure is 1T-based (Figure 1a), but is distorted such that there are two non-equivalent Ta and three non-equivalent Te positions in the unit cell (24); we find TaSe 2-x Te x in this polymorph to be non-superconducting down to 0.4 K.
We report the structures and superconducting properties of TaSe  x Te x emerges and shows a T c of 0.5 -0.7 K. At higher Te substitutions (1.8 ≤ x ≤ 2), TaSe 2-x Te x changes again, into the monoclinic polymorph, and shows normal metallic behavior to 0.4 K. We argue that the isovalent Te/Se substitution acts to tune the anisotropy of the layers, inducing the 3R to 1T transition, consistent with what has been proposed previously (25).The driving force for the 2H to 3R transition currently remains obscure.

Results and Discussion
The polycrystalline samples of TaSe 2-x Te x were prepared as described in the experimental section. In the composition range of 0.02 ≤ x ≤ 0.35, the samples have the non-centrosymmetric rhombohedral 3R structure (R3m, space group #160), evidenced by their powder X-ray diffraction (PXRD) patterns. The 3R-stucture of the materials in this composition range is also confirmed by single crystal X-ray diffraction and electron diffraction. The detailed crystallographic data determined from the quantitative structure refinements of a single crystal of the 3R phase are summarized in Tables 1 and 2. In the refined crystal structure of 3R TaSe 1.7 Te 0.3 , Ta atoms are located in trigonal prisms surrounded by a random mixture of Te and Se atoms. Refining the structure with the ideal 3R atomic coordinates leaves a significant positive residual electron density that is unaccounted for by the model. By investigating the detailed electron density maps, layer stacking faults, which are a common occurrence in crystal structures of this type, were observed through the presence of an "extra" atom site in the tantalum layer, occupied at the 5% level; thus about 5% of the layers in 3R TaSe 1.7 Te 0.3 crystal studied quantitatively are stacked in a way that violates the ideal A-B-C stacking of the 3R phase (e.g. in an A-B-A-B stacking); the remaining 95% of the structure is unfaulted 3R. The PXRD pattern for 3R-TaSe 1.65 Te 0.35 is shown in the main panel of Figure 1b. The inset of Figure 1b shows the variation of the room-temperature lattice parameters (a and c) for 3R-TaSe 2-x Te x in its full range of composition stability; the lattice parameters a and c increase from a = 3.436(1) Å c = 19.207(9) for x = 0.02 to a = 3.465(1) Å and c = 19.600(7) Å for x = 0.35. For higher Te contents, a mixture of MX 2 structures is encountered until x = 0.8, where TaSe 2-x Te x changes into the 1T-polymorph (P-3m1, space group #164), which exists until x = 1.3. The powder diffraction pattern for one of the 1T compositions is shown in Figure 1c and the inset to Figure 1c shows the variation of the room-temperature lattice parameters (a and c) for 1T-TaSe 2-x Te x over its full range of composition stability. For this phase, the lattice parameters increase linearly from a = 3.5468(4) Å c = 6.6344(7) Å (x = 0.8) to a = 3.6008(2) Å and c = 6.5356(10) Å (x = 1.3). A mixture of MX 2 phases is encountered again at higher x until the distorted 1T structure of TaTe 2 is found for 1.8 ≤ x ≤ 2.0.
To compare the structural stability regimes of the different forms of TaSe 2- x Te x , it is most instructive to divide the c axis lattice parameter by the number of layers in the stacking repeat, n, and then compare the reduced c/a ratios (c/n)/a to define the structural characteristics of single MX 2 layers. Figure 1d shows the x variation of the reduced c/a ratio, (c/n)/a, for the 2H (n = 2, x = 0), 3R (n = 3, 0.02 ≤ x ≤ 0.35) and 1T (n = 1, 0.8 ≤ x ≤ 1.3) phases. As shown in the plot, the (c/n)/a ratio increases with increasing x in the 3R form, with a at the 2H to 3R transition, and is always less than the ideal ratio, which for the close-packed trigonal-prismatic arrangement is considered to be 2.0 (26). The (c/n)/a ratio collapses for the 1T polymorph, and changes relatively little with increasing x. In this case, the (c/n)/a ratios are slightly larger than the ideal value of 1.633 (26). The (c/n)/a ratio where the 3R polytype becomes unstable and the 1T polymorph becomes stable is consistent with expectations for MX 2 phases, as has been described by others (26).
To determine whether CDWs are present in the 3R and 1T forms of TaSe 2-x Te x , the materials were studied at low temperatures by electron diffraction and scanning tunneling microscopy (STM). The temperature dependent electron diffraction patterns obtained from single-crystal domains (Figures 2a and 2b) reveal critical information about the CDWs in both materials. In the 3R form, a strong CDW appears on cooling TaSe 2-x Te x below ambient temperature. The CDW gives rise to extra peaks in the electron diffraction patterns, which are already weakly visible at 330 K. For 3R TaSe 1.9 Te 0.1 , the superlattice peaks are first in incommensurate positions and weak but then sharpen and intensify significantly on reducing temperature until at 10 K they are sharp and strong, indicating that the CDW is well defined and ordered over a long range at low temperatures. The incommensurate locations of the spots in reciprocal space at higher temperatures shows that first there is an ICDW phase with the q vector larger than 0.33. The ICDW diffraction spots then change position on cooling until they lock into nearly commensurate positions, q ~ 0.32, at around 100 K. The illuminated areas from which the electron diffraction patterns were obtained is relatively large, with beam diameters greater than 300 nm. The small value of incommensuration observed in the low temperature locked-in CDW phase, which is less than 0.01 from the commensurate value of 0.33, may come from defects and domain walls in the low temperature CDW phase; as the STM topographic images show (see below) the CDW is locked into a commensurate relationship with the underlying atomic lattice over the vast majority of the material, we thus consider it to be a commensurate CDW with a wave vector of q = 0.33. The 10 K electron diffraction pattern shown in Figure (Fig. 3a-b), that in TaSe 1.7 Te 0.3 is moderately masked by the disorder (Fig. 3d-e). However, the Fourier transform of the topographic images for both samples (Fig. 3c and 3f) unambiguously reveals the primary peaks of the CCDW at q 1 = q 2 = 0.33. Hence, the CDW is present for both high and low Te contents in the 3R phase. Remarkably, even in the presence of the strong disorder we observe that the phase of the CDW is unperturbed and only a single domain CDW appears in the field of view (~40 nm x 40 nm). Furthermore, the STM data indicates that the apparent tripling of the cell by the CDW in both in-plane directions deduced from the electron diffraction patterns is not due to the overlap of single-q domains in different orientations; i.e. it is a 2D CDW. Further, the diffracted spots from the CDW phase are visible in single crystal diffraction experiments at 100 K; the data shows that the q vector is in-plane only; there is no c axis component. The data therefore show that for the CCDW in the 3R polymorph, q 1 = 0.33, q 2 = 0.33, and q 3 = 0). The CCDW state the 2H-TaSe 2 polytype is also reported have the wave-vectors q 1 = q 2 = 0.33 and q 3 = 0 (27,28). In other words, in both 2H and 3R polytypes of TaSe 2 , the electronic instabilities that lead to the CCDWs are two-dimensional in character.
The situation is somewhat different for the 1T polymorph (Figures 2b and 2d).
In this case, weak, diffuse superlattice spots whose intensities and positions are relatively independent of temperature between 10 and 330 K are observed in the electron diffraction experiments. Here the in-plane q vector is further from the commensurate value, near q = 0.30, but the weakness and diffuseness of the spots makes them invisible in a single crystal diffraction experiment and so we have no information about their c axis component. These spots likely represent an ICDW phase that is ordered over short spatial distances and stable over the whole temperature range studied. Alternatively they may have a chemical origin, such as might occur due to short range Se/Te ordering. Further work will be required to determine which is the case.
We next consider the electronic properties of the phases. The main panel of Figure 4a shows the temperature dependence of the normalized electrical resistivity, (/ 300K ), for the polycrystalline 3R-TaSe 2-x Te x (0.02 ≤ x ≤ 0.35) samples. All the 3R samples have resistivities below 10 mohm cm at 300 K with a metallic temperature dependence, and all show the signature of the lock-in to the CCDW phase at around 100 K through a change in slope of (T). A similar change in slope of (T) is observed in many TMDC systems at the onset of a CDW that localizes some but not all of the electrons at the Fermi surface (29). A look at the derivative of the (T) curves (inset of Figure. 4d) indicates that the impact of the CDW lock-in transition, which appears to have a temperature that is independent of Te content, weakens with increasing Te content in the 3R phase. Correspondingly, a superconducting transition is found (inset of Figure 4a). With higher Te doping in the 3R phase, the superconducting transition temperature (T c ) increases. The maximum superconducting transition temperature is 2.4 K for 3R-TaSe 1.65 Te 0.35 . T c is a factor of approximately 20 higher than is observed in the 2H form. The superconducting transition is clearly observed through the presence of a full shielding signal in the temperature dependent magnetization measurements (Figure 4d).
The main panel of Figure 4b shows the temperature dependence of the normalized electrical resistivity (/ 300K ) for the polycrystalline samples of 1T-TaSe 2- x Te x (0.8 ≤ x ≤ 1.3). In this case, the residual-resistivity-ratio is very small, RRR =  300K / n < 1.3, which we take as a reflection of the substantial Se-Te disorder present. N(E F ) and λ ep values for the 3R polytype may be why it has dramatically higher Tc than the 2H polytype, but why these parameters are different in the 2H and 3R polytypes is not currently known.
Finally, the overall behavior of the TaTe x Se 2-x system is summarized in the structural and electronic phase diagram shown in Figure 5. On Te substitution for Se in 2H-TaSe 2 , the 3R polytype is immediately stabilized and in TaSe 2-x Te x exists in the range of 0.02 ≤ x ≤ 0.35. 3R TaSe 2-x Te x shows the coexistence of a CDW and superconductivity in this composition range. The superconducting transition temperature is found to maximize at the limit of the structural stability of the 3R phase, x = 0.35. The maximum T c , 2.4 K, is 17 times higher than that for 2H-TaSe 2 .
We conclude that 3R-TaSe 2-x Te x can be considered as a good candidate for characterizing the balance between CDW formation and superconductivity in the 3R polytype of the layered TMDCs. With further Te doping, the 3R-polytype becomes unstable as its (c/n)/a ratio approaches the structural stability limit expected for TMSCs, and the 1T polymorph, with octahedral rather than trigonal prismatic coordination for the Ta, emerges at x = 0.8. The 1T polytype structure exists from x = 0.8 to 1.3. 1T-TaSe 2-x Te x-x displays superconducting transitions below 1 K and the T c does not change significanly with x. 1T-TaSe 2-x Te x appears to display a weak, short range ordered incommensurate CDW at temperatures as high as 330 K, but further work will be necessary to support that conclusion. The monoclinic polymorph exists over a limited composition range in TaSe 2-x Te x , from x = 1.8 to 2.0; it is metallic but not superconducting above 0.4 K.
In conclusion we have shown that the TaSe 2-x Te x system, based on the isoelectronic substitution of Te for Se in TaSe 2 , is an excellent venue for investigating the influence of polytypism and polymorphism on superconductivity in the layered transition metal dichalcogenides. It may be that the major impact of the change in polytype from 2H to 3R in this system, which increases Tc by a factor of 17, is in the the final analysis actually still a 2D effect. The 3R polytype is stable for larger (c/n)/a ratios for a single layer than it is possible to obtain in the 2H polytype: (c/n)/a for the 2H polytype is 1.84 whereas for the maximum Tc of the 3R polytype it is 1.89. If this is the primary reason for the difference in Tc, then it indicates a remarkable sensitivity of Tc to the aspect ratio of the TaX 6 triangular prisms that make up the single layers.
Alternatively, the superconducting transition temperature may depend on differences in the electronic structure that arise as a result of the differences between a two layer stacking repeat and a three layer stacking repeat, in other words how the nominally 2D Fermi surface is modulated along c, the perpendicular direction, by the stacking.
Further investigation will be required to resolve which of these is the case, or whether a different strong influence on Tc is present. The Tc of the 1T polymorph is intermediate between that of the 2H and the 3R, with a Tc a factor of 5 larger than that in the 2H variant at approximately the same (c/n)/a, but as the TaX 6 coordination scheme is octahedral rather than trigonal prismatic in this polymorph, different aspects of its electronic structure may determine its superconducting transition temperature. Further study of this system may prove to be of significant interest. TaSe  Intensities were extracted and corrected for Lorentz and polarization effects with the SAINT program. Empirical absorption corrections were accomplished with SADABS which is based on modeling a transmission surface by spherical harmonics employing equivalent reflections with I > 2σ(I) (35)(36)(37)(38).With the SHELXTL package, the crystal structures were solved using direct methods and refined by full-matrix least-squares on F 2 (37). All crystal structure drawings were produced using the program VESTA (38).