# Pressure enhancement of CDW formation in VSe2; the role of Coulomb correlations

Denis Jerome, Richard H Friend, D.M. Schleich, P. Molinié

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Denis Jerome, Richard H Friend, D.M. Schleich, P. Molinié. Pressure enhancement of CDW formation in VSe2; the role of Coulomb correlations. Solid State Communications, 1978. hal-04983129

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PRESSURE ENHANCEMENT OF CHARGE DENSITY WAVE FORMATION IN VSe₂;
THE ROLE OF COULOMB CORRELATIONS*

R.H. Friend† and D. Jérôme

Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
and

D. M. Schleich‡ and P. Molinié

Laboratoire de Chimie Minérale A, B.P. 1044, 44037 Nantes, France

*(Received 23 February 1978 by P.G. de Gennes)*

We have followed the pressure dependence of the onset and lock-in CDW transitions in VSe₂ by measurements of resistivity and Hall effect up to 30 kbar. (The onset transition appears as a break in the slope of the resistivity, and the lock-in as ~1% temperature hysteresis). Both transition temperatures rise at 0.8 K kbar⁻¹. We attribute this behaviour to pressure broadening of the *d* conduction band in the presence of strong electron Coulomb repulsion.

THE STUDY of charge density wave (CDW) formation in the group V transition metal dichalcogenides [1, 2] has been largely concentrated on the 4d and 5d metals, and the only vanadium dichalcogenide that can easily be prepared, IT VSe₂, has received less attention. It is however an interesting material in that CDW formation is relatively weak, and that the CDW superlattice is different from that observed in the IT tantalum dichalcogenides. Conductivity and susceptibility measurements [3–6] show an anomaly at around 110 K, and electron diffraction [7] shows the appearance of a 4 × 4 incommensurate superlattice at this temperature. The superlattice is initially 2% incommensurate, but at 40 K has become commensurate. The weak anomaly in resistivity at the normal–incommensurate transition, and the nature of the incommensurate–commensurate lock-in transition, where the superlattice does not rotate to form the commensurate phase as in IT TaSe₂ and IT TaSe₂, are more common with the 2H polytype of TaSe₂ [8] than with the IT polytypes. There is little change in transport properties at the lock-in transition in 2H TaSe₂, no more than 1% temperature hysteresis in the resistivity, which has been measured to follow the lock-in transition under pressure [9]. We have measured the resistivity and Hall coefficient of VSe₂ under pressure as a function of temperature to follow

the CDW formation. We have found temperature hysteresis in the resistivity, similar to that in 2H TaSe₂, at around 70 K at 1 bar, which is at the temperature of the lock-in seen in electron diffraction on the crystals we used [10]. Thus we have been able to follow both the normal–incommensurate, onset transition and the lock-in transition under pressure. In contrast to all the IT and 2H polytypes previously investigated [9, 11–15], CDW formation in VSe₂ is enhanced under pressure. We relate this behaviour to the narrow *d* band in VSe₂ [16] and the larger Coulomb interaction between the conduction electrons derived from the 3d V orbitals, compared to 4d Nb and 5d Ta.

VSe₂ is always found to grow metal rich, with the excess V taking up sites between the layers, and possessing localised moments which show up as a Curie tail in the low temperature magnetic susceptibility. Measurements of susceptibility can, therefore, be used to characterise batches of VSe₂. Crystals used for these experiments were grown by selenium vapour transport in a temperature gradient of 830 → 780°C, with excess Se present, conditions similar to those used by van Bruggen and Haas [4]. The magnetic susceptibility of ground crystals was measured using a Faraday balance and is shown in Fig. 1. The CDW onset transition shows up as a fall in susceptibility below ~100 K. Fitting the Curie tail to $χ = χ_i + C/T$, where $χ_i$ is the almost temperature independent intrinsic susceptibility gives $χ_i = 2.47 × 10⁻⁴$ emu mole⁻¹ and $C = 4.32 × 10⁻³$ emu K mole⁻¹; the fitted curve is shown as the solid line in Fig. 1. Also shown is $χ_{exp} - C/T$, which represents the intrinsic behaviour of the VSe₂.

To determine the V excess from the value of C

<footnote>* Work supported in part by DGRST Contract No. 77-7-0549.</footnote>

<footnote>† Permanent address: Cavendish Laboratory, Cambridge, U.K.</footnote>

<footnote>‡ Supported in part by N.S.F. Grant No. 39737.</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 3. Hall effect vs temperature for VSe₂ at 1 bar and 8 kbar.</figcaption></figure>

Under pressure both transitions move to higher temperatures, as is shown in Fig. 2. The range of hysteresis for the helium gas experiment at 8 kbar is still narrow, and the extended temperature range at higher pressures may be a consequence of slight pressure inhomogeneities in the isopentane/isoamylalcohol mixture which is solid at these temperatures and pressures. Hall effect measurements are shown in Fig. 3; at 1 bar the data is similar to that previously reported [4, 5], and at 8 kbar the low temperature rise which signals the onset transition has moved to a higher temperature. The pressure-temperature phase diagram is shown in Fig. 4. The onset transition rises at 0.8 K kbar⁻¹; the lock-in transition also rises at a similar rate although the change in width of the hysteresis loop with pressure prevents precise determination of the rate.

It is not possible to say much about the behaviour of the lock-in transition without knowledge of how the incommensurability of the CDW superlattice changes with pressure. We note however that in contrast to VSe₂, the lock-in transition of 2H TaSe₂ at 90 K falls rapidly and is suppressed entirely above 15 kbar [9].

The pressure dependence of the onset transition is more significant, and is a further example of the anomalous behaviour of VSe₂. The CDW transition temperature in VSe₂ at 1 bar is appreciably lowered from the value that may be expected from comparison with the IT Nb and Ta dichalcogenides (see Table 1), and either the application of pressure, or Nb doping [24] raises this temperature.

<figure><img src="image_4.png" /><figcaption>Fig. 4. Onset (●) and lock-in (■) CDW transition temperatures in VSe₂ as a function of pressure, as derived from the resistivity measurements of Fig. 2. The onset was taken as the temperature at which the resistivity first deviates from its high temperature behaviour. For the lock-in transition, ■ is at the temperature of the maximum resistivity hysteresis, and the bars indicate the limits at which the hysteresis has fallen to 20% of its maximum value.</figcaption></figure>

Recent photoemission experiments [16] have shown an occupied *d* bandwidth of only ~0.3 eV, and it is this very much narrower *d* band that is found in IT TaSe₂ and IT TaSe₂ (see Table 1) that distinguishes VSe₂ from the 4*d* and 5*d* materials. This narrow *d* band does not appear in the band structure calculated by Wooley and Wexler [25], who find little difference between VSe₂ and TaSe₂. However VSe₂ has an anomalously high *c/a* ratio, of 1.821 [26], and so a strong trigonal distortion of the octahedral field around the V, which splits the *t*₂g triplet into a *d*<sub>xy</sub>, *d*<sub>x²-y²</sub> doublet and a *d*<sub>z²</sub> level. For such a trigonal distortion the *d*<sub>z²</sub> level will be lowest [27], and if the splitting of the *d*<sub>z²</sub> and *d*<sub>xy</sub>, *d*<sub>x²-y²</sub> levels is a substantial fraction of the band broadening of these levels, the lowering of the half occupied *d*<sub>z²</sub> band can be interpreted as the driving force of a band Jahn-Teller distortion [28]

which increases the *c/a* ratio. Note that the increased occupation of the *d* band from Li intercalation decreases the *c/a* ratio, in spite of the Li introduced between the layers. This is consistent with occupation of the *d*<sub>xy</sub>, *d*<sub>x²-y²</sub> levels by the Li valence electron which will take place if the Coulomb repulsion *U* for the *d* states is larger than the *d*<sub>z²</sub> bandwidth.

Coulomb repulsion between the conduction electrons
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