Polytypism, polymorphism, and superconductivityin TaSe2−xTexHuixia Luoa,1, Weiwei Xiea, Jing Taob, Hiroyuki Inouec, András Gyenisc, Jason W. Krizana, Ali Yazdanic, Yimei Zhub,and Robert Joseph Cavaa,1

aDepartment of Chemistry and cJoseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544; and bDepartment ofCondensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973

Contributed by Robert Joseph Cava, February 9, 2015 (sent for review January 14, 2015; reviewed by J. Paul Attfield and Maw-Kuen Wu)

Polymorphism in materials often leads to significantly differentphysical properties—the rutile and anatase polymorphs of TiO2 area prime example. Polytypism is a special type of polymorphism,occurring in layered materials when the geometry of a repeatingstructural layer is maintained but the layer-stacking sequence ofthe overall crystal structure can be varied; SiC is an example ofa material with many polytypes. Although polymorphs can haveradically different physical properties, it is much rarer for polytyp-ism to impact physical properties in a dramatic fashion. Here westudy the effects of polytypism and polymorphism on the super-conductivity of TaSe2, one of the archetypal members of the largefamily of layered dichalcogenides. We show that it is possible toaccess two stable polytypes and two stable polymorphs in theTaSe2−xTex solid solution and find that the 3R polytype showsa superconducting transition temperature that is between 6 and17 times higher than that of the much more commonly found 2Hpolytype. The reason for this dramatic change is not apparent, butwe propose that it arises either from a remarkable dependence ofTc on subtle differences in the characteristics of the single layerspresent or from a surprising effect of the layer-stacking sequenceon electronic properties that are typically expected to be domi-nated by the properties of a single layer in materials of this kind.

superconductivity | polytypism | polymorphism | dichalcogenide |charge-density wave

The MX2 layered transition-metal dichalcogenides (TMDCs,M = Mo, W, V, Nb, Ta, Ti, Zr, Hf, or Re and X = Se, S, or

Te), have long been of interest due to the rich electronic prop-erties that emerge due to their low dimensionality (1–9). Struc-turally, these compounds can be regarded as having stronglybonded (2D) X–M–X layers, with M in either trigonal prismaticor octahedral coordination with X, and weak interlayer X–Xbonding of the van der Waals type. Many of these materialsmanifest charge-density waves and competition between charge-density waves (CDWs) and superconductivity, e.g., refs. 5–9.Among the TMDCs, the 2H (H: hexagonal) polytype of tantalumdiselenide (2H-TaSe2) is considered one of the foundationalmaterials (8–18), showing a transition from a metallic phase toan incommensurate charge-density wave (ICDW) phase at 123K, followed by a “lock-in” transition to a commensurate charge-density wave (CCDW) phase at 90 K. It finally becomes a su-perconductor with a rather low transition temperature (Tc) of0.15 K. Although detailed studies have been performed on thephysics of CDWs and superconductivity in 2H-TaSe2 (16–18),a comparative study of the superconductivity of the polytypesand polymorphs of TaSe2 from the chemical perspective has notbeen done.TaSe2 is highly polymorphic, possibly the most polymorphic of

the TMDCs (19). In some of its forms, notably the 2H and 3R(R: rhombohedral) polytypes (Fig. 1A), Ta is found in trigonalprismatic coordination in Se-Ta-Se layers that are stacked alongthe c axis of the hexagonal (or rhombohedral) cell. The 2H and3R polytypes differ only in their stacking periodicity—the struc-ture repeats after two layers in the 2H form and three layers in the

3R form (20–22). The 3R form can be synthesized, but it is not thestable variant (the 2H form is) and so has been the subject of littlestudy. In one of the other polymorphs, the 1T (T: trigonal) type,Ta is found in octahedral coordination in the Se-Ta-Se layers andthe layer stacking along the c axis of the trigonal cell such that thestructure repeats after only one layer (23) (Fig. 1A). Again, the 1Tform has not been the subject of much study. Here we show thatthe 3R and 1T polymorphs are both quite stable in the TaSe2−xTexsystem and that they are both superconducting. For pure TaTe2,the monoclinic structure is 1T based (Fig. 1A), but is distortedsuch that there are two nonequivalent Ta and three nonequivalentTe positions in the unit cell (24); we find TaSe2−xTex in thispolymorph to be nonsuperconducting down to 0.4 K.We report the structures and superconducting properties of

TaSe2−xTex for 0 ≤ x ≤ 2. The 2H, 3R, 1T, and monoclinic dis-torted 1T-structure forms were successfully synthesized. Onlya small amount of Te doping (x = 0.02) changes 2H-TaSe2 intothe 3R polytype. Within the 3R polytype, TaSe2−xTex shows thecoexistence of a CDW and superconductivity above 0.4 K for0.1 ≤ x ≤ 0.35. The Te-rich limit of the 3R-TaSe1.65Te0.35 polytypeshows the highest Tc in the system, 2.4 K, which is 17 times higherthan that of 2H-TaSe2. For 0.8 ≤ x ≤ 1.3, 1T-type TaSe2−xTexemerges and shows a lower Tc, of 0.5–0.7 K. At higher Te sub-stitutions (1.8 ≤ x ≤ 2), TaSe2−xTex changes again, into themonoclinic polymorph, and shows normal metallic behavior to0.4 K. We argue that the isovalent Te/Se substitution acts to tunethe anisotropy of the layers, inducing the 3R to 1T transition,consistent with what has been proposed previously (25). The drivingforce for the 2H to 3R transition currently remains obscure.

Significance

Although polymorphs of a substance can often have dramati-cally different physical properties, polytypes, which occurwhen the geometry of a structural layer is maintained but thenumber of layers in the layer-stacking sequence is changed,rarely do. Here we find, using random substitution of Te forsome of the Se to induce structural changes in TaSe2, a classiclayered dichalcogenide, so that the transition temperature tosuperconductivity (Tc) is significantly different for differentpolytypes and polymorphs and especially differs when goingfrom one polytype to another. This observation implies eithera surprising sensitivity of Tc to the layer-stacking sequence ora similarly surprising sensitivity of Tc to the small changes inlayer geometry that accompany the change in polytype.

Author contributions: H.L., J.T., A.Y., Y.Z., and R.J.C. designed research; H.L., W.X., J.T.,H.I., A.G., J.W.K., A.Y., and Y.Z. performed research; H.L., W.X., J.T., H.I., A.G., J.W.K., A.Y.,Y.Z., and R.J.C. analyzed data; and H.L., W.X., J.T., H.I., A.G., J.W.K., A.Y., Y.Z., and R.J.C.wrote the paper.

Reviewers: J.P.A., University of Edinburgh; and M.-K.W., Academia Sinica.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1To whom correspondence may be addressed. Email: rcava@princeton.edu or huixial@princeton.edu.

E1174–E1180 | PNAS | Published online March 3, 2015 www.pnas.org/cgi/doi/10.1073/pnas.1502460112

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Results and DiscussionThe polycrystalline samples of TaSe2−xTex were prepared asdescribed in Methods. In the composition range of 0.02 ≤ x ≤0.35, the samples have the noncentrosymmetric rhombohe-dral 3R structure (R3m, space group 160), evidenced by theirpowder X-ray diffraction (PXRD) patterns. The 3R structure of thematerials in this composition range is also confirmed by single-crystal X-ray diffraction and electron diffraction. The detailedcrystallographic data determined from the quantitative structurerefinements of a single crystal of the 3R phase are summarized inTables 1 and 2. In the refined crystal structure of 3R-TaSe1.7Te0.3,Ta atoms are located in trigonal prisms surrounded by a randommixture of Te and Se atoms. Refining the structure with the ideal3R atomic coordinates leaves a significant positive residual electrondensity that is unaccounted for by the model. By investigating thedetailed electron density maps, layer-stacking faults, which area common occurrence in crystal structures of this type, were ob-served through the presence of an “extra” atom site in the tantalumlayer, occupied at the 5% level; thus about 5% of the layers in the3R TaSe1.7Te0.3 crystal studied quantitatively are stacked in a waythat violates the ideal A-B-C stacking of the 3R phase (e.g., in anA-B-A-B stacking); the remaining 95% of the structure is unfaulted

3R. The PXRD pattern for 3R-TaSe1.65Te0.35 is shown in the mainpanel of Fig. 1B. For higher Te contents, a mixture of MX2 struc-tures is encountered until x = 0.8, where TaSe2−xTex changes intothe 1T polymorph (P-3m1, space group 164), which exists until x =1.3. The powder diffraction pattern for one of the 1T compositionsis shown in the main panel of Fig. 1C. Reitveld refinements of thePXRD data (Methods) were used to specify the z coordinates of the(Se,Te) atom positions across the 3R and 1T solid solutions,allowing the determination of the TaX2 and van der Waals layerthicknesses separately.To compare the structural stability regimes of the different

forms of TaSe2−xTex, it is most instructive to divide the c-axislattice parameter by the number of layers in the stacking repeat,n, and then compare the thus-obtained reduced c/a ratios, (c/n)/a,to define the structural characteristics of single MX2 layers(“slabs” in the following) and their associated van der Waalsgaps. In Fig. 1 B and C, Insets show the x variation of the reducedc/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, respectively. Asshown in the plots, the (c/n)/a ratio increases with increasing x inthe 3R form, with a discontinuity at the 2H to 3R transition, andis always less than the ideal ratio, which for the close-packed

2H-TaSe2

3R-TaSe1.7Te0.3 Monoclinic-TaTe2

1T-TaSeTe

TaTeSe

A

Inte

rsity

(Arb

. Uni

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(Arb

. Uni

tes)

3R-TaSe2-xTex2H-TaSe2

B C

E F G

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3R-TaSe2-xTex

3R1T

2H

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)

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(Å)

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x in TaSe2-xTex

x in TaSe2-xTexx in TaSe2-xTexx in TaSe2-xTex

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(Å)

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vdW

G (

Å)2H3R1T

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1.00.0 0.2 0.4 0.6 0.8 1.2 1.41.00.0 0.2 0.4 0.6 0.8 1.2 1.41.00.0 0.2 0.4 0.6 0.8 1.2 1.4

3.73.53.33.12.92.72.5

10 20 30 40 50 60 70 80 902 (degree)

10 20 30 40 50 60 70 80 90

6.86.76.66.56.46.36.2

3.83.73.63.53.43.33.2

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1.840.8 0.9 1.0 1.1 1.2 1.3

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(c/n

a) /

Fig. 1. Structural characterization and analysis of the polytypes and polymorphs of TaSe2−xTex. (A) The crystal structures of 2H-TaSe2, 3R-TaSe1.65Te0.35,1T-TaSeTe, and monoclinic TaTe2. (B) Powder X-ray diffraction pattern for 3R-TaSe1.65Te0.35. Inset shows the reduced lattice parameter ratio, (c/n)/a, where n =number of layers per cell, for 2H-TaSe2 (38) and 3R-TaSe2−xTex. (C) Powder X-ray diffraction pattern for 1T-TaTeSe. Inset shows the reduced lattice parameterratio, (c/n)/a, for 1T-TaSe2−xTex. (D) The variation of in-plane lattice parameter, a, with x for 2H-, 3R-, and 1T-TaSe2−xTex. (E) The variation of reduced stacking-direction lattice parameter, c/n, with x for 2H-, 3R-, and 1T-TaSe2−xTex. (F) The variation of the TaX2 slab thickness, ((c·(Δz)), with x for 2H-, 3R-, and 1T-TaSe2−xTex.(G) The variation of the van der Waals gap (vdWG) thickness with x for 2H-, 3R-, and 1T-TaSe2−xTex.

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trigonal-prismatic arrangement is considered to be 2.0 (26).The (c/n)/a ratio collapses for the 1T polymorph and changesrelatively little with increasing x. In this case, the (c/n)/a ratiosare slightly larger than the ideal value of 1.633 (26). The (c/n)/aratio where the 3R polytype becomes unstable and the 1T poly-morph becomes stable is consistent with expectations for MX2phases, as has been described by others (26).Fig. 1 D and E shows the variations of the room-temperature

in-plane lattice parameters (a) and the reduced lattice parame-ters (c/n) in the stacking direction for the 2H, 3R, and 1T formsof TaSe2−xTex over the full range of composition stability. Anoverall trend toward larger a and c values with increasing x isobserved across the whole family as larger Te replaces Se, butthe composition dependence is also generally different in thedifferent structural forms and there are discontinuities at thetransitions between forms. A mixture of MX2 phases is en-countered at higher x until the distorted 1T structure of TaTe2 isfound for 1.8 ≤ x ≤ 2.0.It is instructive to look at the changes in structure within the

TaSe2−xTex series in more detail by considering separatelythe composition dependencies of the TaX2 slab thickness and thevan der Waals gap thickness. This is shown in Fig. 1 F and G,where the variation of the TaX2 slab thickness, [(c·(Δz), where cis the c-axis length and Δz is the difference in refined z coor-dinates for the X positions above and below the Ta layer] andthat of the similarly determined van der Waals gap (vdWG)thickness are presented. As shown in Fig. 1F, the thickness of theTaX2 slab increases essentially continuously with increasing xacross all forms, with a change in slope ongoing from the 3R to 1Tpolymorphs. In contrast, the van der Waals gap thickness changesvery little with x in either the 3R or the 1T polytypes, with a sig-nificant collapse of thickness on passing from the 3R to 1T poly-morphs. The factors determining the behaviors observed in Fig. 1F and G are not presently known.To determine whether CDWs are present in the 3R and 1T

forms of TaSe2−xTex, the materials were studied at low temper-atures by electron diffraction and scanning tunneling microscopy(STM). The temperature-dependent electron diffraction patternsobtained from single-crystal domains (Fig. 2 A and B) revealcritical information about the CDWs in both materials. In the 3Rform, a strong CDW appears on cooling TaSe2−xTex below am-bient temperature. The CDW gives rise to extra peaks in theelectron diffraction patterns, which are already weakly visible at

330 K. For 3R TaSe1.9Te0.1, the superlattice peaks are first inincommensurate positions and weak but then sharpen and in-tensify significantly on reducing temperature until at 10 K they aresharp and strong, indicating that the CDW is well defined and or-dered over a long range at low temperatures. The incommensuratelocations of the spots in reciprocal space at higher temperaturesshow that first there is an ICDW phase with the q vector larger than0.33. The ICDW diffraction spots then change position on coolinguntil they lock into nearly commensurate positions, q ∼ 0.32, ataround 100 K. The illuminated areas from which the electron dif-fraction patterns were obtained are relatively large, with beamdiameters greater than 300 nm. The small value of incommensu-ration observed in the low-temperature locked-in CDW phase,which is less than 0.01 from the commensurate value of 0.33, maycome from defects and domain walls in the low-temperature CDWphase; as the STM topographic images show (see below), the CDWis locked into a commensurate relationship with the underlyingatomic lattice over the vast majority of the material. We thusconsider this to be a commensurate CDW with a wave vector ofq = 0.33. The 10-K electron diffraction pattern shown in Fig. 2Ais an indication of the quality of this low-temperature CCDWphase. At the lock-in transition, the intensity of the diffractedspots from the CDW increases dramatically, an indication of itsstrengthening in the CCDW state. The temperature-dependentcharacteristics of the CDW in 3R TaSe1.9Te0.1 obtained from theelectron diffraction study are summarized in Fig. 2C. Thus, inanalogy to the 2H form of TaSe2, 3R-TaSe1.9Te0.1 first has anICDW and then locks in to a CCDW phase on further cooling.The q vectors of the CCDW phase, q1 = q2 = 0.33, indicate a tri-pling of the in-plane unit cell along both a1 and a2 by the CDW.STM measurements on 3R-TaSe1.9Te0.1 and on 3R-TaSe1.7Te0.3

provide additional characterization of the CCDW phase. Topo-graphic images on the atomic scale (Fig. 3) display the in-plane unitcell tripling in real space on the surface of both samples below theCDW transition temperature. Whereas the CDW superlattice inTaSe1.9Te0.1 is clearly visible (Fig. 3 A and B), that in TaSe1.7Te0.3is moderately masked by the disorder (Fig. 3 D and E). However,the Fourier transform of the topographic images for both samples(Fig. 3 C and F) unambiguously reveals the primary peaks of theCCDW at q1 = q2 = 0.33. Hence, the CDW is present for bothhigh and low Te contents in the 3R phase. Remarkably, even inthe presence of the strong disorder due to the Se/Te solid so-lution, we observe that the phase of the CDW is unperturbed andonly a single-domain CDW appears in the field of view (∼40 nm ×40 nm). Furthermore, the STM data indicate that the apparenttripling of the cell by the CDW in both in-plane directions de-duced from the electron diffraction patterns is not due to theoverlap of single-q domains in different orientations; i.e., it isa 2D CDW. Further, the diffracted spots from the CDW phaseare visible in single-crystal diffraction experiments at 100 K; thedata show that the q vector is in plane only; there is no c-axiscomponent. The data therefore show that for the CCDW in the3R polymorph, q1 = 0.33, q2 = 0.33, and q3 = 0. In the CCDWstate the 2H-TaSe2 polytype is also reported have the wave vec-tors q1 = q2 = 0.33 and q3 = 0 (27, 28). In other words, in both 2H

Table 1. Single-crystal crystallographic data for3R-TaSe1.70Te0.30 at 296(2) K

Formula TaSe1.70Te0.30

F.W., g/mol 353.46Space group; Z R3m (no.160); 3a, Å 3.4603(7)c, Å 19.523(4)V, Å3 202.44(9)Absorption correction MultiscanExtinction coefficient 0.006(3)μ, mm−1 66.441θ range, ° 3.130–29.555hkl ranges −4 ≤ h,k ≤ 4

−27≤ l ≤ 27No. reflections; Rint 714; 0.0451No. independent reflections 189No. parameters 14R1; wR2 (all I) 0.0530; 0.1347Goodness of fit 1.284Diffraction peak and hole, e−/Å3 7.885; –3.371

The numbers in parentheses are the standard error of the refined parameters.

Table 2. Atomic coordinates and equivalent isotropicdisplacement parameters of TaSe1.70Te0.30

Atom Wyckoff Occupancy x y z Ueq

Ta1 3a 0.95(1) 0 0 0.2931(1) 0.009(1)Ta2 3a 0.05(1) 2/3 1/3 0.293(3) 0.009(1)Se/Te1 3a 0.85/0.15 1/3 2/3 0.2059(3) 0.012(1)Se/Te2 3a 0.85/0.15 1/3 2/3 0.3804(3) 0.011(1)

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor (Å2).

The numbers in parentheses are the standard error of the refined parameters.

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and 3R polytypes of TaSe2, the electronic instabilities that lead tothe CCDWs are 2D in character.The situation is somewhat different for the 1T polymorph (Fig. 2

B and D). In this case, weak, diffuse superlattice spots whose in-tensities and positions are relatively independent of temperaturebetween 10 K and 330 K are observed in the electron diffractionexperiments. Here the in-plane q vector is farther from the com-mensurate value, near q = 0.30, but the weakness and diffusenessof the spots make them invisible in a single-crystal diffraction ex-periment and so we have no information about their c-axis com-ponent. These spots likely represent an ICDW phase with q1 = q2 =0.30 and q3 = 0 that is ordered over short spatial distances andstable over the whole temperature range studied. Alternatively theymay have a chemical origin, such as might occur due to short-rangeSe/Te ordering. Further work will be required to determine whichis the case.We next consider the electronic properties of the phases. The

main panel of Fig. 4A shows the temperature dependence of thenormalized electrical resistivity, (ρ/ρ300K), for the polycrystalline3R-TaSe2−xTex (0.02 ≤ x ≤ 0.35) samples. All of the 3R sampleshave resistivities below 10 mohm/cm at 300 K with a metallictemperature dependence, and all show the signature of the lock-in to the CCDW phase at around 100 K through a change inslope of ρ(T). A similar change in slope of ρ(T) is observed inmany TMDC systems at the onset of a CDW that localizes somebut not all of the electrons at the Fermi surface (29). A look at thederivative of the ρ(T) curves (Fig. 4D, Inset) indicates that theimpact of the CDW lock-in transition, which appears to havea temperature that is independent of Te content, weakens withincreasing Te content in the 3R phase. Correspondingly, a super-conducting transition is found (Fig. 4A, Inset). With higher Tedoping in the 3R phase, the superconducting transition temperature(Tc) increases; the superconductivity is first found at low temper-

atures and increases to a maximum of 2.4 K for 3R-TaSe1.65Te0.35,substantially higher than that observed in the 2H form. Thesuperconducting transition is clearly observed through the presenceof a full shielding signal in the temperature-dependent magneti-zation measurements (Fig. 4D).The main panel of Fig. 4B shows the temperature dependence

of the normalized electrical resistivity (ρ/ρ300K) for the poly-crystalline samples of 1T-TaSe2−xTex (0.8 ≤ x ≤ 1.3). In this case,the residual-resistivity ratio is very small, RRR = ρ300K/ρn < 1.3,which we interpret as a reflection of the substantial Se-Te dis-order present. No signature of a CDW lock-in transition is seen inρ(T), consistent with the electron diffraction data. At low tem-peratures, a clear, sharp (ΔTc < 0.1 K) drop of ρ(T) is observed,signifying the onset of superconductivity (Fig. 4B, Inset). Thesample with x = 1 shows the highest Tc, 0.73 K. Finally, Fig. 3Cpresents the temperature dependence of the normalized resistiv-ity for polycrystalline samples of the monoclinic polymorph ofTaSe2−xTex (1.8 ≤ x ≤ 2). This variant shows metallic behavior,similar to what has been previously reported (24), with no super-conducting transition down to 0.4 K.Further information on the electronic properties and super-

conductivity in the 3R and 1T variants of TaSe2−xTex was ob-tained from specific heat measurements. The main panels ofFig. 4 E and F show the temperature dependence of the zero-field specific heat, Cp./T vs. T2, for 3R-TaSe1.65Te0.35 and 1T-TaSe1.2Te0.8. The normal state-specific heat at low temperatures(but above Tc) obeys the relation of Cp = γT + βT3, where γ and βdescribe the electronic and phonon contributions to the heat ca-pacity, respectively, the latter of which is a measure of the Debyetemperature (θD). By fitting the data in the temperature range of2–10 K, we obtain the electronic specific heat coefficients γ = 7.25mJ·mol−1·K−2 for 3R-TaSe1.65Te0.35 and γ = 2.91 mJ·mol−1·K−2

for 1T-TaSe1.2Te0.8 and the phonon specific heat coefficients

A

B

C

D

(110)(110)(000)(000) (210)(210)

-

T = 10 k T = 78 K T = 125 K

T = 180 K

T = 10 K T = 83 K

T = 223 K T = 295 K

0.025

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0 100 200 300Temperature (K)

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Fig. 2. Characterization of the charge-density waves in the 3R and 1T polymorphs. Temperature dependence of the incommensurate CDW state in the a–bplane is shown. (A) temperature dependence of electron diffraction patterns of polycrystalline 3R-TaSe1.7Te0.3. (B) Temperature dependence of electrondiffraction patterns of polycrystalline 1T-TaTeSe. (C and D) CDW vector qCDW as a function of temperature for (C) 3R-TaSe1.6Te0.3 and (D) 1T-TaSeTe.

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β = 0.93 mJ·mol−1·K−4 for 3R-TaSe1.65Te0.35 and β =1.82 mJ·mol−1·K−4 for 1T-TaSe1.2Te0.8. Using these values of β, weestimate the Debye temperatures by the relation θD= (12π4nR/5β)1/3,

where n is the number of atoms per formula unit (n = 3) and Ris the gas constant; the θD values are found to be 184 K for3R-TaSe1.65Te0.35 and 147 K for 1T-TaSe1.2Te0.8. As shown in

A

B C

D

E F

Fig. 3. (A–F) Visualization of the charge-density wave on the surface of 3R-TaSe1.9Te0.1 (A–C) and 3R-TaSe1.7Te0.3 (D–F) by STM. (A and B) Real space to-pographic images of (A) 300-Å × 300-Å and (B) 60-Å × 60-Å areas on the cleaved a–b surface of TaSe1.9Te0.1 [VBias = −800 mV, (A) I = 100 pA, and (B) I = 60 pA]at T = 48 K, which show the tripling of the in-plane unit cell. The CDW remains unchanged around the bright spots on the surface, which are associated withthe substituted Te atoms. (C) The Fourier transform of a 440-Å × 440-Å large topographic image reveals wave vectors corresponding to the atomic modu-lation (black circles) and q vectors of the commensurate charge-density wave phase (q1 = q2 = 0.33, red circles). Higher harmonics of q1 and q2 are marked bygray circles. (D–F) Similar topographic images (D and E) of the surface of TaSe1.7Te0.3 at VBias = 300 mV, I = 200 pA, and T = 27 K and (F) Fourier transform ofa 490-Å × 490-Å large area. The CDW is clearly observed despite the disorder induced by the higher Te substitution.

x=0.35x=0.3x=0.25x=0.2x=0.15x=0.1

TCDW0.0004

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1 2 3 4

T (K)0.0 0.3 0.6 0.9 1.2 1.5TLO

FC

ZFC

M’ (

emu)

T (K)

x=1.9x=1.8

1.4

1.2

1.0

0.8

0.6

0.4

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0.0008

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T (K)

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100

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00 20 40 60 80 100

151050-5

-10

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0.0 1.0 2.0 3.0

0.0002

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0.0000

50 100 150

0.000006

0.000004

0.000002

0.00000

T (K)

TaSe1.65Te0.35H = 10Oe

0.0000

-0.0005

-0.0010

-0.0015

-0.0020

-0.0025

-0.00301.8 2.0 2.2 2.4 2.6 2.8 3.0

6420

-2

Tc = 0.6 K

1T-TaSe2-xTex

TaSe1.2Te0.8

x=2

Fig. 4. Characterization of the electronic properties of TaSe2−xTex. (A) The temperature dependence of the ratio (ρ/ρ300K) for 3R-TaSe2−xTex. (Inset) Enlarged viewof low-temperature region (0.4–3 K), showing the superconducting transition. (B) The 1T-TaSe2−xTex. (Inset) Enlarged view of low-temperature region (0.4–0.8 K)showing the superconducting transition. (C) Monoclinic TaSe2−xTex (1.8 ≤ x ≤ 2). (Inset) Enlarged view of the low-temperature region showing the absence ofsuperconductivity. (D) The temperature dependence of dc magnetic susceptibility for 3R-TaSe1.65Te0.35. (Inset) Enlarged view of dρ/dT of 3R-TaSe2−xTex showingCDW lock in temperature (TLO). (E) The temperature dependence of specific heat Cp of 3R-TaSe1.65Te0.35, presented in the form of Cp/T vs. T2 (main panel) and Cel/Tvs. T (Inset). (F) The temperature dependence of specific heat Cp of 1T-TaSe1.2Te0.8, presented in the form of Cp/T vs. T2 (main panel) and Cel/T vs. T (Inset).

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Fig. 4 E and F, Insets, both materials display a large specific heatjump at Tc. The superconducting transition temperatures arein excellent agreement with the Tcs determined in the ρ(T)measurements. We estimate ΔC/Tc = 8.7 mJ·mol−1·K−2 for 3R-TaSe1.65Te0.35 and ΔC/Tc = 3.93 mJ·mol−1·K−2 for 1T-TaSe1.2Te0.8.The normalized specific heat jump values ΔC/γTc are found to be1.20 for 3R-TaSe1.65Te0.35 and 1.35 1T-TaSe1.2Te0.8, which are nearthat of the Bardeen–Cooper–Schrieffer (BCS) weak-coupling limitvalue (1.43), confirming bulk superconductivity. Using the Debyetemperature (θD) and the critical temperature Tc and assuming thatthe electron–phonon coupling constant (λep) can be calculated fromthe inverted McMillan equation (30),

λep =1:04+ μ p lnðθD=1:45TcÞ

ð1− 0:62μ p ÞlnðθD=1:45TcÞ− 1:04:

The values of λep obtained are 0.64 for 3R-TaSe1.65Te0.35 and0.51 for 1T-TaSe1.2Te0.8 and suggest weak coupling supercon-ductivity. With the Sommerfeld parameter (γ) and the electron–phonon coupling (λep), the density of states at the Fermi level canbe calculated from NðEFÞ= ð3=π2k2Bð1+ λepÞÞγ. This yields N(EF) =1.88 states/eV formula unit for optimal 3R-TaSe1.65Te0.35 andN(EF) = 0.82 states/eV formula unit for 1T-TaSe1.2Te0.8. These com-pare with λep = 0.4 and N(EF) = 1.55 for the 2H-TaSe2 (31). Thesomewhat larger N(EF) and λep values for the 3R polytype maybe why it has dramatically higher Tc than the 2H polytype, butwhy these parameters are different in the 2H and 3R polytypesis not currently known.Fig. 5A shows the variation of the superconducting Tc with the

reduced c/a ratio (c/n)/a, for 2H-TaSe2, 3R-TaSe2−xTex (0.1 ≤ x ≤0.35), and 1T-TaSe2−xTex (0.8 ≤ x ≤ 1.3), where n = number oflayers in the stacking repeat, and c and a are the unit cellparameters. Tc increases smoothly with (c/n)/a in the 3R form,but is constant in the 1T form. The 2H, 3R, and 1T forms areclearly distinguished in this plot, showing that the super-conducting Tc is not a simple function of the overall structuralcharacteristics across the whole family. The distinction betweenthe polymorphs and polytypes is seen even more dramatically inFig. 5B, where Tc is plotted as a function of the aspect ratio ofthe TaX2 slab across the whole family. Tc increases nearly im-possibly steeply with the slab aspect ratio in the 3R form before

saturating, but varies very little with this important characteristicof a single layer in the 1T form. A dramatic distinction is seenbetween the 2H and 3R polytypes on this plot. Finally, theoverall behavior of the TaTexSe2-x system is summarized in thestructural and electronic phase diagram shown in Fig. 5C. On Tesubstitution for Se in 2H-TaSe2, the 3R polytype is immediatelystabilized and in TaSe2−xTex exists in the range of 0.02 ≤ x ≤0.35. The 3R-TaSe2−xTex shows the coexistence of a CDWand superconductivity in this composition range. The super-conducting transition temperature is found to maximize at thelimit of the structural stability of the 3R phase, x = 0.35. Themaximum Tc, 2.4 K, is substantially higher than that for 2H-TaSe2. We conclude that 3R-TaSe2−xTex can be considered asa good candidate for characterizing the balance between CDWformation and superconductivity in the 3R polytype of the lay-ered TMDCs. With further Te doping, the 3R polytype becomesunstable as its (c/n)/a ratio approaches the structural stabilitylimit expected for TMSCs, and the 1T polymorph, with octahe-dral rather than trigonal prismatic coordination for the Ta,emerges at x = 0.8. The 1T polytype structure exists from x = 0.8to 1.3. The 1T-TaSe2−xTex-x displays superconducting transitionsbelow 1 K and the Tc does not change significantly with x. The1T-TaSe2−xTex appears to display a weak, short-range orderedincommensurate CDW at temperatures as high as 330 K, butfurther work will be necessary to support that conclusion. Themonoclinic polymorph exists over a limited composition range inTaSe2−xTex, from x = 1.8 to 2.0; it is metallic but not super-conducting above 0.4 K.In conclusion we have shown that the TaSe2−xTex system,

based on the isoelectronic substitution of Te for Se in TaSe2, isan excellent venue for investigating the influence of polytypismand polymorphism on superconductivity in the layered transitionmetal dichalcogenides. It may be that the major impact of thechange in polytype from 2H to 3R in this system, which increasesTc by a factor of 6–17, is in the final analysis actually still a 2Deffect. The 3R polytype is stable for larger (c/n)/a and slabthickness ratios for a single layer than it is possible to obtain inthe 2H polytype. If one of these is the primary reason for thedifference in Tc, then it indicates a remarkable sensitivity of Tcto the aspect ratio of the TaX6 triangular prisms that makeup the single layers, evidenced especially in Fig. 5B. Alternatively,

(c⋅(Δz))/a

TaSe2-xTex

2H3R1T

T c (K

)

2.82.42.01.61.20.80.40.0

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T c (K

)

T c (K

)

Mix

ed p

hase

Mix

ed p

hase

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x in TaSe2-xTex

1T-SC3R-S

C2H

Mon

oclin

ic m

etal

C2/m

Superconductivity in TaSe2-xTex dichalogenides

P-3m1R3m

2H3R1T

(c/n)/a

3R

1T

TaSe2-xTex

2H

3.0

2.5

2.0

1.5

1.0

0.5

0.01.84 1.85 1.86 1.87 1.88 1.89

3R

2H1T

A C

B

Fig. 5. Structural and superconducting phase diagram for TaSe2−xTex. (A) The variation of the superconducting Tc with the reduced c/a ratio (c/n)/a, for 2H-TaSe2, 3R-TaSe2−xTex (0.1 ≤ x ≤ 0.35), and 1T-TaSe2−xTex (0.8 ≤ x ≤ 1.3), where n = number of layers in the stacking repeat, and c and a are the unit cellparameters. The different superconducting forms are very clearly distinguished in this plot. (B) The variation of the superconducting Tc with the TaX2 slabthickness, (c·(Δz)), for 2H-TaSe2, 3R-TaSe2−xTex (0.1 ≤ x ≤ 0.35), and 1T-TaSe2−xTex (0.8 ≤ x ≤ 1). Again, the different superconducting forms are very clearlydistinguished. (C) The composition stability ranges of the 2H, 3R, 1T, and monoclinic MX2 forms in TaSe2−xTex and the dependence of Tc on x. The TaX2

coordination polyhedra are highlighted. Single-phase regions are shown in pink, and multiple-phase regions are shown in blue.

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the difference in superconducting transition temperature of thepolytypes, similarly suggested to be quite different in Fig. 5B, maydepend on differences in the electronic structure that arise asa result of the differences between a two-layer stacking repeat anda three-layer stacking repeat, in other words how the nominally 2DFermi surface is modulated along c, the perpendicular direction,by the layer stacking. Further investigation by both experimentand electronic structure calculations will be required to resolvewhich of these is the case or whether a different strong influenceon Tc is present. The Tc of the 1T polymorph is intermediatebetween that of the 2H and the 3R, with Tc a factor of 5 largerthan that in the 2H variant, but as the TaX6 coordination schemeis octahedral rather than trigonal prismatic in this polymorph,different aspects of its electronic structure may determine itssuperconducting transition temperature. Further study of thissystem may prove to be of significant interest.

MethodsPolycrystalline samples of TaSe2−xTex (0 ≤ x ≤ 2) were synthesized in twosteps by solid-state reaction. First, mixtures of high-purity fine powders of Ta[99.8 atomic (atm) %], Te (99.999 atm%), and Se (99.999 atm%) in the ap-propriate stoichiometric ratios were thoroughly ground, pelletized, andheated in sealed evacuated silica tubes at a rate of 1 °C/min to 700 °C andheld there for 48 h. Subsequently, the as-prepared powders were reground,repelletized, and sintered again, heated at a rate of 3 °C/min to 1,000 °C andheld there for 48 h. Single crystals were grown by the chemical vapor trans-port (CVT) method with iodine as a transport agent. One gram as-preparedpowders of TaSe2−xTex mixed with 50 mg iodine was sealed in evacuated silicatubes and heated for 1 wk in a two-zone furnace, where the temperatures ofsource and growth zones were fixed at 1,050 °C and 1,000 °C, respectively. Theidentity and phase purity of the samples were determined by powder X-raydiffraction (PXRD) (Rigaku; Cu Kα radiation, graphite diffracted beam mono-chromator). Unit cell parameters and the z coordinate of the Se+Te atompositions (the only structural variable) were refined from the powder dif-fraction data through use of the FULLPROF diffraction suite (32). For the 3Rpolymorph, the Se/Te positions were constrained to be symmetric at ±z aroundthe Ta positions, yielding regular TaX6 prisms. Measurements of the temper-ature dependence of the electrical resistivity were heat capacity performed in

a Quantum Design Physical Property Measurement (PPMS). For the super-conducting samples, Tc was taken as the intersection of the extrapolation ofthe steepest slope of the resistivity ρ(T) in the superconducting transition re-gion and the extrapolation of the normal state resistivity (ρn) (33). Magneti-zation measurements as a function of temperature and applied field werecarried out in a Quantum Design Magnetic Property Measurement (MPMS).Selected resistivities for TaSe2−xTex (0.1 ≤ x ≤ 0.25; 0.7 ≤ x ≤ 1.3; and 1.8, 1.9,and 2) and heat capacities for TaSe1.65Te0.35 and TaSe1.2Te0.8 were measured inthe PPMS equipped with a 3He cryostat.

Single crystals from the samples were mounted on the tips of glass fibers.Room temperature intensity data were collected on a Bruker Apex II dif-fractometer with Mo radiation Ka1 (λ = 0.71073 Å). Data were collected overa full sphere of reciprocal space with 0.5° scans in ωwith an exposure time of10 s per frame. The 2θ range extended from 4° to 60°. The SMART softwarewas used for data acquisition. Intensities were extracted and corrected forLorentz and polarization effects with the SAINT program. Empirical ab-sorption corrections were accomplished with SADABS, which is based onmodeling a transmission surface by spherical harmonics, using equivalentreflections with I > 2σ(I) (34–37). With the SHELXTL package, the crystalstructures were solved using direct methods and refined by full-matrix leastsquares on F2 (36). All crystal structure drawings were produced using theprogram VESTA (37).

Before the STMmeasurements, the samples were cleaved and transportedto the microscope in ultrahigh vacuum. The experiments were performed onTaSe1.9Te0.1 at 48 K and on TaSe1.7Te0.3 at 27 K with a home-built variabletemperature STM. Temperature-dependent electron diffraction measure-ments were performed on a JEOL 2100F microscope at Brookhaven NationalLaboratory equipped with a liquid-helium cooling sample holder.

ACKNOWLEDGMENTS. This research was primarily supported by the ArmyResearch Office (ARO) Multidisciplinary University Research Initiative (MURI)on superconductivity, Grant FA-9550-09-1-0953. ARO MURI Grant FA-9550-10-1-0553 supported the single-crystal diffraction work, and the Depart-ment of Energy (DOE) Basic Energy Sciences (BES) supported the powderdiffraction refinements through Grant DE FG02-08ER46544. The electrondiffraction study at Brookhaven National Laboratory was supported bythe DOE BES, by the Materials Sciences and Engineering Division underContract DE-AC02-98CH10886, and through the use of the Center for Func-tional Nanomaterials. The STM work was supported under the ARO-MURIProgram W911NF-12-1-0461 and the National Science Foundation GrantDMR-1104612.

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