Anomalous features of the CDW transition in metallic 2H dichalcogenides

The metallic dichalcogenides of transition metals which cystallise in the trigonal prismatic 2H structure, are considered as a model familyfor the study of chargedensity-wave transitions of the metal-metal type. We review different properfies and their evolution in the series: transport, specific heat, magnetic susceptibility, soft phonon dynamics. For temperatures higher than the transition temperature, Td many characters underline the departure from the normal metal behaviour as well as from the behaviour resulting from the presence of the simple soft mode predicted by weak-coupling theories. A phenomenological analysis rather suggests for this family a very strong coupling mechanism involving local vibronic pseudo spins, narrow-band character and proximity to an orderdisorder transition. Metallic dichalcogenides of transition metals, MX2 (M=Nb,Ta; X=S,Se), which crystallise in the trigonal prismatic 2H lamellar structure are well-known for undergoing charge-densitywave (CDW) transitions linked to their two-dimensional character [I-31. The CDW transition temperatures, Td, are 123 K, 80 K and 33 K for TaSe2, TaS2 and NbSe2, respectively, while NbS2 undergoes no phase transition. The accompanying incommensurate lattice distortion which also develops below Td is however close to the commensurate modulation wave-vector Q=(a*/3,0,0). The modulation is indeed triple-Q and the displacements of ionic centres belong to the XI symmetry ( this predominantly consists in a longitudinal motion of the cations). The preceding characters are shared by all the compounds undergoing the CDW transformation. Continuous efforts in structural studies over many years revealed also a variety of additional features [4,5] which confirm the intimate similarities existing between these compounds. The mechanism of the transition is thought to mainly result from the electron-phonon interaction in presence of quasi-2D "nesting" conditions. The different band structure calculations [6] for these systems agree about a Fermi Surface made of quasi-cylindrical pockets, the first ones elongated along HKH edges and the last one with its axis along ATA in the Brillouin zone. A van Hove anomaly resulting from the connection between the zone centre isoenergy surfaces and the edges ones is also possible but its distance from the Fermi level, EF, is still uncertain. The total width of the predominantly dz2 character band near EF is more than 2eV. A detailed theoretical investigation of the electron-phonon interaction in those systems was carried out by MOTIZUKI and co-workers [7] on.the basis of an effective tight binding model. This study show the importance of both the nesting conditions and of the q-dependent Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993224 JOURNAL DE PHYSIQUE IV electron-phonon coupling coefficient for causing the lattice instability. This approach, a weak coupling one in essence, obtained good success in particular by predicting the right symmetry for the soft phonon mode. However it failed to provide a satisfactory evaluation of the different observed Td's. This can be due to limits in the calculation but most probably results from more basic reasons involving the need for a short coherence length model [8] and a strong coupling approach [9]. The strong coupling nature of the present CDW's received renewed support recently owing to the use of STM spectroscopy which indicates very large ratios between the CDW gap and Td: 2A/kTd= 15.2,15.4 and 23.9 for TaSe2, TaS2 and NbSe2, respectively [lo]. These values remain however much lower than the I.R. reflectivity data [ll]: 46 in the case of TaSe2. In the following, we review selected experimental topics which could help for a better understanding of the CDW formation in this model family. 2.Macroscopic properties. At first sight, transport properties of 2H-MX2 compounds appear to follow closely the normal metal behaviour. This contrasts with the IT-polytypes for which case the CDW transition is of the metal-non metal type. In 2H systems both the distorted and the undistorted phase, above and below Td, are fully metallic. At lower temperatures, the resistivity g(T) behaves like ~3 or ~5 for Nb and Ta compounds respectively, as expected for d metals [12]. For distorted systems, but not in NbS2, a large positive magneto resistance is observed belonr Td which is due to magnetic breakdown effects in the reconstructed band structure [13]. Near Td, a small anomaly can be detected in e(T) as a result of the CDW pseudo-gap formation which is confirmed by the strong increase in the absolute value of the Hall coefficient, RH [12]. Above Td however, several difficulties raise in comparison with the above normal aspects. The first problem concerns the resistivity of TaSe2 and, to a less extent of TaS2, for which an additional constant contribution is present above Td. The presence of a correlated minimum in the phonon dominated thermal conductivity is strongly suggestive of a pseudo-spin mechanism for scattering both electrons and phonons [14]. Transport experiments can be then accounted for by an additional constant relaxation rate which is progressively reduced as the CDW order sets in below Td. The analysis of the specific heat supports the proposed scheme which basically represents the CDW transition as an order-disorder one [14,15]. The form of the specific heat anomaly near Td in TaSe2 is well accounted for by a jump contribution plus a gaussian fluctuation one reflecting the short coherence length (k-10A) [16]. This was considered by McMILLAN as an argument in favour of a "local soft mode" [8]. Our approach goes one step further by considering the order-disorder character of the transition which agrees well with the variation of the transition entropy AS#Rln2, once one refers to the unit cell of the distorted phase i.e. nine times that of the high temperature crystallographic phase. This view implies that the local soft mode has not a continuous character but it is rather of a pseudo-spin nature with a double degeneracy. A detailed picture of the atomic displacements and of the accompanying CDW modulation was proposed [14]. However, the above picture breaks down for the other compounds in the series. First, the transition entropy becomes significantly less than the order-disorder value. Instead, it scales with the transition temperature [15]. Secondly, a refined investigation of g(T) shows the existence of "saturation" effects, i.e. a negative curvature, occurring in the higher temperature range. This effect is most pronounced for NbS2. This behaviour is not fortuitous as shown by the thermoelectric power, S [15]. The latter has negative values at room temperature for all compounds. This contradicts the positive Hall effect and the exclusively positive charge carriers predicted by band calculation. In addition, large absolute values are achieved