Rich structural phase diagram and thermoelectric properties of layered tellurides Mo1-xNbxTe2

MoTe2 is a rare transition-metal ditelluride having two kinds of layered polytypes, hexagonal structure with trigonal prismatic Mo coordination and monoclinic structure with octahedral Mo coordination. The monoclinic distortion in the latter is caused by anisotropic metal-metal bonding. In this work, we have examined the Nb doping effect on both polytypes of MoTe2 and clarified a structural phase diagram for Mo1-xNbxTe2 containing four kinds of polytypes. A rhombohedral polytype crystallizing in polar space group has been newly identified as a high-temperature metastable phase at slightly Nb-rich composition. Considering the results of thermoelectric measurements and the first principles calculations, the Nb ion seemingly acts as a hole dopant in the rigid band scheme. On the other hand, the significant interlayer contraction upon the Nb doping, associated with the Te p-p hybridization, is confirmed especially for the monoclinic phase, which implies a shift of the p-band energy level. The origin of the metal-metal bonding in the monoclinic structure is discussed in terms of the d electron counting and the Te p-p hybridization.

Transition metal dichalcogenides (TMDs) MX 2 (X = S, Se, Te) with layered structure have been extensively studied due to their wide variety of electronic properties such as superconductivity, large thermoelectric effect, and anomalous magnetoresistance. [1][2][3] In addition, recent experimental progress on TMDs exfoliated down to a monolayer or a few layers have stimulated great interest in their potential applications to spin-valleytronics and optoelectronics. 4,5 When containing heavy elements and lacking inversion symmetry, a strong spin-orbit coupling yields the interplay of spin and valley degrees of freedom.
The diverse electronic properties of layered TMDs are enriched by structural polymorphism, which are differentiated by the chalcogen coordination of metal ion and by the stacking sequence of MX 2 layers. 1,6,7 The polytypes commonly obtained are 1T (CdI 2 -type structure) and 2H structures, consisting of the edge-shared octahedra and the trigonal prisms of MX 6 , respectively (see Fig. 1). The integer of the polytypes denotes the number of MX 2 layers per unit cell and the capital letter stands for the symmetry of Bravais lattice such as trigonal (T), hexagonal (H), and rhombohedral (R). Spurred by the seminal works on monolayer MoS 2 , 8,9 3R-MoS 2 without inversion symmetry has been revealed to show the valley-dependent photoluminescence even in multilayers. 10 The group V and VI transition-metal (TM) ditellurides crystallize mostly in 1T polytype.
Among them, MoTe 2 is an exceptional TM ditelluride adopting two kinds of polytypes, 2H polytype (so called α-MoTe 2 ) 11 and distorted 1T polytype (so called β-MoTe 2 ). 12 α-MoTe 2 shows semiconducting behavior and transforms into the high-temperature metallic phase β-MoTe 2 at 820−880 • C. 13,14 In α-MoTe 2 , the trigonal prismatic coordination causes the crystal field splitting for a non-bonding d band, by which a narrow band formed by d z 2 orbitals splits off. Given that the p-d hybridization is negligibly small, the nominal valence of the molybdenum ion is 4+ with a d 2 electron counting. Thus, the Fermi level is expected to reside inside the gap with fully occupying the d z 2 orbital. 15,16 On the other hand, the structural and electronic properties of β-MoTe 2 , which can be obtained as a metastable phase by quenching from above 900 • C, are not so straightforward. β-MoTe 2 at room temperature crystallizes in monoclinically distorted 1T polytype (P 2 1 /m) with semimetallic band structure. 12 In each MoTe 2 layer, zigzag chains made of metal-metal bonding are formed along the b axis, giving rise to a considerable shift of Mo ions along the a axis from the center of each octahedron (See Fig. 3(a)). The metal-metal bonding is also observed in NbTe 2 having distorted 1T structure (C2/m) with double zigzag chains. 17 In this paper, we renamed the distorted 1T polytypes for β-MoTe 2 and NbTe 2 as 1T' and 1T" polytypes, respectively (note that the number of 1T'-MoTe 2 layers per unit cell is 2). The origin of the chain formations has been discussed in terms of the Fermi surface nesting in the d band and electron-phonon coupling. 18,19 However, the situation is not so simple because of a strong p-d hybridization inherent to tellurides with 1T structure.
In this work, structure and transport properties of Mo 1−x Nb x Te 2 are studied to see how Nb doping modifies lattice and electronic structures of the two polytypes, 1T'-and 2H-MoTe 2 . We have established a detailed structural phase diagram containing the newly identified 3R polytype. Considering the thermoelectric measurements and first principles calculations, the effect of the Nb doping is simply interpreted in terms of the rigid band shift of the Fermi level. On the other hand, an enhancement of the Te p-p hybridization affecting the valence band structure is signified by a significant interlayer contraction especially for Nb-doped 1T'-MoTe 2 with metal-metal bonding. We discuss the important role of the Te p orbitals as well as the d electron counting in the structure and electronic properties of Nb-doped MoTe 2 .
All polycrystalline samples were synthesized by solid state reaction in evacuated quartz tubes. The mixtures of stoichiometric amounts of elements, Mo (purity 99.9 %), Nb (purity 99.9 %), and Te (purity 99.999 %), in powder form were heated at 1050 -1100 • C for 12 h, followed by cooling down to room temperature in 3 h. The obtained samples were ground, pelletized, and then annealed at selected temperatures between 800 and 1100 • C for 12 h.
The annealed samples were obtained after water quenching, except for 2H-MoTe 2 which was cooled to room temperature by furnace cooling. Powder x-ray diffraction (XRD) patterns were corrected on a Bruker D8 advance diffractometer using Cu Kα radiation. For transport measurements, the samples were cut into rectangular shape in the typical dimensions of 5 × 1 × 0.3 mm 3 . The thermopower and thermal conductivity were measured by a conventional steady-state method with a temperature difference of less than 1 K between the voltage electrodes.
Electronic structure calculations were performed within the context of density functional theory using the Perdew-Burke-Ernzerhof exchange-correlation functional modified by the Becke-Johnson potential, as implemented in the WIEN2K program 20 . Relativistic effects, including spin-orbit coupling, were fully included. The muffin-tin radius of each atom R MT was chosen such that its product with the maximum modulus of reciprocal vectors K max become R MT K max = 7.0. The structural parameters were taken from the reference 15 Table I. Let us describe the important features of XRD profiles for samples annealed at 1050 • C.
The h0l reflections around 2θ ∼ 35 • are useful to discriminate the 3R phase from the 2H phase. However, those reflections for x = 0.4−0.6 suffer from a significant broadening, while the 00l reflections remain sharp. It has been reported that Ta 1−x M x Se 2 (M = Re, Os), of which d electron counting deviates from an integer number, has a mixed-layer structure consisting of an incoherent stacking of 2H and 3R layers. The volume fraction of 2H and 3R varies depending on the chemical composition. 21 The mixed-layer structure (or equivalently intergrowth) is detectable as the peak broadening of the h0l reflections originated from either 2H or 3R polytypes. The same feature is found for the XRD patterns of compounds with x = 0.4−0.6 obtained by annealing at 1050 • C. The existence of the mixed-layer structure in the present system reflects the proximity of the free energies between the 2H and 3R polytypes in addition to the entropy contribution at high temperatures. Besides the peak broadening except for the 00l reflections, the similar peak broadening is also seen for the 1T' phase with x = 0 and 0.2, indicating the mixed-layer structure with a small amount of 2H layer forming during the quenching process. The undistorted 1T structure (P 3m1) potentially existing at high temperatures have not been obtained presumably because of the unquenchable nature or the incompatibility with the d electron counting of d 1 − d 2 . The 3R polytype exists as a meta-stable state in a narrow temperature-composition range and is more stable than the 2H polytype at high temperatures. As mentioned above, the 3R phase obtained in this study contains a minor portion of the 2H layers as mixed-layers. The relative stability between 2H and 3R polytypes has been discussed for sulfides and selenides. The theoretical studies for MoS 2 and MoSe 2 have pointed out that the 2H and 3R phases are energetically almost degenerate but the former is more favorable than the latter. 25 It has been reported for MoS 2 that the 2H phase transforms into the 3R phase at high pressures above 4 GPa and at high temperatures above 1900 • C. 26 Accordingly, the extent of the stable composition for 3R-Mo 1−x Nb x Te 2 is expected to be enlarged by the application of high pressure as well. This expectation is supported by the experimental fact that 3R-Mo 0.4 Nb 0.6 Te 2 has a higher crystal density compared to that of 2H polytype in the same composition.
To study the relation between the structural and the electronic properties of Mo 1−x Nb x Te 2 , structural parameters calculated from the lattice constants are plotted as a function of Nb content x in Figs. 3(d)-(j). Note that the lattice parameters for compounds with a minor phase or the mixed-layer structure were refined as two phase system, and the data of the major phase only were presented in the plots. As confirmed in Figs 1T'-MoTe 2 P 2 1 /m 4 6.3126(4) 3.4711 (2)