# Evidence for a connection between charge density waves and the pressure enhancement of superconductivity in 2H-NbSe2

Claude Berthier, Philippe Molinié, Denis Jérôme

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Claude Berthier, Philippe Molinié, Denis Jérôme. Evidence for a connection between charge density waves and the pressure enhancement of superconductivity in 2H-NbSe2. Solid State Communications, 1976, 18 (9-10), pp.1393-1395. 10.1016/0038-1098(76)90986-8. hal-04980182

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Distributed under a Creative Commons Attribution 4.0 International License
EVIDENCE FOR A CONNECTION BETWEEN CHARGE DENSITY WAVES AND THE PRESSURE ENHANCEMENT OF SUPERCONDUCTIVITY IN 2H-NbSe₂*

C. Berthier,† P. Molinié‡ and D. Jérome

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

(Received 22 December 1975 by P.G. de Gennes)

The pressure dependence of the onset of charge density waves (CDW) in 2H-NbSe₂ has been studied by resistivity measurements up to 35 kbar. It demonstrates that the pressure enhancement of T_c is due to the presence of CDW in the crystal, and stops when T_CDW becomes smaller than T_c at P = 36 kbar.

BECAUSE of the two-dimensional character of their structure, transition metal dichalcogenides (TX₂) are good candidates for the observation of charge density waves (CDW).¹ In the 2H polytype of NbSe₂, the onset of a triple incommensurate CDW at T_CDW = 33.5 K has been established by neutron experiments.² So this compound is particularly interesting since it exhibits both the highest superconducting temperature T_c (7-7.3 K) and the lowest T_CDW observed in the TX₂ family. Furthermore, it has been widely reported that the T_c in 2H-NbSe₂ is strongly enhanced by pressure (5 × 10⁻⁵ K/bar).³⁻⁶ The measurements of Smith et al.³ were made up to 140 kbar; T_c was observed to increase rapidly with pressure up to about 35 kbar, but to remain nearly constant above that pressure, suggesting a structural transformation. The dependence of T_c on lattice instabilities has been of constant interest in the last few years, especially in the A-15 compounds⁷,⁸ in which a martensitic transformation occurs at a temperature T_M above T_c. A correlation between the pressure dependence of T_M or T_CDW and T_c is suggested by experiment in V₃Si,⁹ Nb₃Sn¹⁰ and 2H-TaS₂.¹¹

In this letter, we report a study of 2H-NbSe₂ at hydrostatic pressures up to 35 kbar by resistivity measurements in the range 4.2-35 K. The 2H-NbSe₂ crystals were grown by vapour phase transport at 780°C with iodine as the transport agent. The polytype was confirmed by X-rays and the value of T_c = 7.11 K¹²

indicates a good stoechiometry. The resistivity was measured parallel to the layers using the d.c. four contacts method. The pressure cell used for this work is the high pressure intensifying cell described elsewhere.¹³

The onset of CDW in 2H-NbSe₂ gives rise to an anomaly in the resistivity which has already been reported at ambient pressure.¹⁴ Its shape, rather broad in temperature, is consistent with a second order transition as is expected theoretically¹⁵ and verified by neutron,² specific heat¹⁴ and NMR¹⁶ studies. In Fig. 1 are shown the resistivity anomalies at various pressures. T_CDW was arbitrarily defined as the point where d²ρ(T)/dT² becomes negative. This can cause a systematic error of at most 1 K in T_CDW. The increase in the residual resistivity for the runs C and D must not be taken too seriously and might be due to some damage introduced in the sample when decreasing the pressure from 35 kbar. The absolute value of ρ was deduced by assuming a value of 100 µΩ cm at room temperature and ambient pressure.¹⁷ In Fig. 2 we have plotted T_CDW and T_c as a function of pressure, including points at ambient pressure and 21 kbar determined by NMR measurements¹⁶ on a sample of the same batch. In the 0-20 kbar range, T_CDW decreases linearly with a coefficient dT_CDW/dP = -0.35 ± 0.05 K/kbar. Using standard thermodynamics for a second order transition, and knowing the jump in specific heat at the transition (ΔCₚ ≈ 1.1 J/mole K),¹⁴ one can deduce the jump in the compressibility 1/V(∂V/∂P)T_CDW = +1.05 ± 0.30 × 10⁻⁶ kbar⁻¹ to be compared to the value of 1.1 × 10⁻⁶ kbar⁻¹ determined by Barmatz et al.¹⁸ for the jump in Young's modulus in the basal plane.

Above 20 kbar, T_CDW decreases much more strongly with pressure. From 34 to 35 kbar, T_CDW drops from 14 to 11 K and must cross T_c(P) around 36 kbar. As T_c is strongly pressure dependent below ~35 kbar and remains nearly constant above that

<footnote>* Work supported in part by the DGRST, contract No. 747 0877.</footnote>

<footnote>† Permanent address: Laboratoire de Spectrométrie Physique, BP 53 38041 Grenoble-Cedex (France).</footnote>

<footnote>‡ Permanent address: Laboratoire de Chimie Minérale A, BP 1044 44037 Nantes Cedex (France).</footnote>

<footnote>§ Laboratoire associé au C.N.R.S.</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1.</figcaption></figure>

pressure up to 140 kbar,³ these results give the first clear evidence that the pressure enhancement of superconductivity in 2H-NbSe₂ (and presumably in other TX₂ compounds), is due to a progressive removal of the CDW in the crystal. This is also confirmed by the absence of pressure enhancement of T_c in 2H-NbS₂⁵ (dT_c/dP ≤ 2 × 10⁻⁶ K/bar) in which no CDW was observed.¹⁹ The comparison between both systems has been invoked already to rule out pressure-dependent Josephson tunnelling between layers.⁵

A correlation between an increase of $T_c$ and the removal of the CDW was already suggested by Murphy *et al.*²⁰ from measurements on 2H-TaS₂ samples intercalated with hydrogen. Nevertheless, addition of hydrogen also changes the filling of the conduction band by charge transfer, and apparently does not fully suppress the CDW, since resistivity anomalies are still present.

It was also claimed by Yamaya *et al.*²¹ that an irreversible, pressure induced phase change occurs at ~1 kbar, the new phase being stable at ambient pressure with a higher $T_c$ and no CDW. This is in complete contradiction with the present measurements, and also our NMR results¹⁶ which show that when releasing pressure from 21 kbar to 1 bar, the CDW is fully restored with the same onset temperature $T_{CDW}$ = 33 K.

We shall now discuss briefly the pressure dependence of $T_{CDW}$ and $T_c$. The decrease of $T_{CDW}$ can be

<figure><img src="image_3.png" /><figcaption>Fig. 2.</figcaption></figure>

explained by an increase of the 3-dimensional character of the band structure²² with pressure, which will reduce the areas of the Fermi surface participating in the nesting; the less good the nesting, the lower will be $T_{CDW}$. A supplementary contribution to the decrease of $T_{CDW}$ with pressure can be expected from the stiffening of the lattice, since the distortion associated with the CDW will then cost more elastic energy. This stiffening should cause at the same time a decrease of $T_c$.²³

Now at the onset of the CDW a gap will open at the Fermi surface in the direction of the spanning vectors.²⁴ This will reduce the density of states at the Fermi level $N(E_F)$ and so decrease the $T_c$; when the pressure is applied, both the areas where the gap opens, and the amplitude of the gap decrease (NMR measurements¹⁶ show that at 21 kbar, the amplitude of the CDW is reduced by the same amount that $T_{CDW}$). So the reduction of $N(E_F)$ will be smaller and $T_c$ will increase.²⁵ Another possible explanation could be the influence on $T_c$ of the soft phonons⁷,²³ associated to the CDW. Such low frequency modes, should be more and more efficient when $T_{CDW}$ approaches $T_c$: one should expect in that case a maximum of $T_c$ around 36 kbar, which is not observed. In fact the increase of $T_c$ between ambient pressure and 35 kbar can be accounted for by a variation only 3 or 4% in $N(E_F)$ or $\lambda$ in the McMillan formula²³ and this is hardly measurable (Measurements of spin lattice relaxation of Nb⁹³ around $T_{CDW}$¹⁶ do not indicate a variation of $N(E_F)$ but the error bars are too large to distinguish such a small variation).

In conclusion, we think that the present results firmly established that the pressure enhancement of $T_c$ in 2H-NbSe₂ is mainly due to a progressive removal of the CDW, which lowers the $T_c$ when present in the crystal; from the pressure dependence of $T_{CDW}$, we can estimate that the CDW fully disappear for pressures larger than 36 kbar, which is just the range in which $T_c$ remains nearly constant. The origin of the interference between both phenomena change in $N(E_F)$,
modification of the electron-phonon coupling, influence of soft modes associated to the onset of the CDW is not yet fully established, and would deserve further experimental and theoretical investigation.

*Acknowledgements* – We wish to thank J. Friedel, M. Weger, P. Garoche and J. Cooper for helpful discussions. We are indebted to G. Malfait for his invaluable technical help.

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