LETTER TO THE EDITOR

# The transport properties of vanadium-doped TiSe₂ under pressure

R H Friend†, S S P Parkin† and D Jérôme‡

† Cavendish Laboratory, Madingley Road, Cambridge, UK

‡ Université Paris-Sud, Laboratoire de Physique des Solids, 91405 Orsay, France

Received 14 May 1982

**Abstract.** Measurements of the temperature dependence of the resistivity of V₀.₀₁Ti₀.₉₉Se₂ and V₀.₀₃Ti₀.₉₇Se₂ at pressures of up to 15 kbar indicate that the tendency for low-temperature carrier localisation at ambient pressure is reduced at high pressure. We consider that this is due to the increase in carrier concentration that results from the increase in p-d band overlap under pressure.

TiSe₂ is a semimetal with a small band overlap between the selenium p valence band and the titanium d conduction band, as is seen directly in angle-resolved photoemission experiments (Traum *et al* 1978, Chen *et al* 1980). At room temperature it exhibits p-type conduction, indicating that the p band holes have a higher mobility than the d band electrons (Di Salvo *et al* 1976). It undergoes a structural phase transition at ~200 K to form a superlattice in which the in-plane and out-of-plane cell constants are doubled (Di Salvo *et al* 1976). This superstructure couples the hole pocket at the Brillouin zone centre to the electron pockets at the zone boundary, and has the effect of reducing the carrier concentration from its high-temperature value of ~3 × 10²⁰ cm⁻³ by a factor of 10 at low temperatures. The change in electronic energy that results from this coupling has been considered as a possible driving mechanism for the distortion.

Preparation of TiSe₂ with excess Ti, which occupies interlayer sites, or substitutional doping with Ta has the effect of increasing the band filling, so that the phase transition, which occurs as a lower temperature than in pure TiSe₂, has a smaller effect on the transport properties. However, substitutional doping with vanadium is found to cause a large increase in low-temperature resistivity, which is particularly strong for a vanadium concentration of 1% (Di Salvo and Waszczak 1978, Lévy and Froidevaux 1979, Lévy 1979). In contrast to Ta, the V present has a local magnetic moment which is either that of d¹ V⁴⁺ or d² V³⁺ (Di Salvo and Waszczak 1978, Schlenker *et al* 1980). The presence of localised d electrons on the V ions prevents the expected increase in band filling, and V-doped TiSe₂ still shows a p-type Hall coefficient, with a value similar to that for pure TiSe₂ (Lévy 1979). For V concentrations of less than ~3% the structural phase transition is still observed, although there is some variation in transition temperature reported (Di Salvo and Waszczak 1978, Lévy 1979, Uchida *et al* 1979, Vaterlaus *et al* 1980). The presence of the random potential from the vanadium and the low carrier concentrations present below the distortion are together sufficient to bring about Anderson localisation
of the remaining carriers. In pure TiSe₂ high pressure has been found to increase the p-d band overlap, bringing about a large increase in carrier concentration (Friend *et al* 1977, 1978, 1982). The transition falls at 1.2 K kbar⁻¹, but as the Fermi surfaces increase in size, a smaller fraction of the carriers are removed by the distortion so that there is a very large increase in low-temperature conductivity. Thus high pressure provides an obvious means of varying the strength of the localisation in V-doped TiSe₂.

We have made measurements of conductivity at high pressure on crystals of V₀.₀₁Ti₀.₉₉Se₂ and V₀.₀₃Ti₀.₉₇Se₂ supplied by F J Di Salvo and F Lévy. Details of growth conditions are given by Di Salvo and Waszczak (1978) and Lévy and Froidevaux (1979). Resistivity measurements were made in the temperature range 4.2 K–300 K and at pressures of up to 15 kbar, achieved in a BeCu pressure cell with isopentane as the high-pressure medium.

Under pressure, the room-temperature conductivity of both materials was found to increase, at rates of 5.6% kbar⁻¹ and 3.2% kbar⁻¹ for V₀.₀₁Ti₀.₉₉Se₂ and V₀.₀₃Ti₀.₉₇Se₂ respectively. These values are lower than the initial slope of 7.7% kbar⁻¹ found for pure TiSe₂ (Friend *et al* 1977). Since the rate of increase of p-d band overlap with pressure

<figure><img src="image_1.png" /><figcaption>**Figure 1.** Resistivity versus temperature for V₀.₀₁Ti₀.₉₉Se₂ at ambient and at high pressure. Runs at 5 kbar, 10 kbar and 15 kbar were performed on the same crystal.</figcaption></figure>

will be the same for these materials, the variation in dlnσ/dp therefore reflects differences in the initial carrier concentration. The closeness of these three values thus provides further confirmation that the degree of band filling in V-doped TiSe₂ is little changed from that in pure TiSe₂.

Resistivity versus temperature curves for V₀.₀₁Ti₀.₉₉Se₂ and V₀.₀₃Ti₀.₉₇Se₂ under pressure are shown in figures 1 and 2 respectively. Room temperature values of the resistivity at ambient pressure are normalised to 10⁻³ Ω cm in accordance with the results of Lévy (1979). It is clear that low-temperature carrier localisation is weakened under pressure for both materials, and for the case of V₀.₀₃Ti₀.₉₇Se₂ fully metallic behaviour is achieved
at 15 kbar. For V<sub>0.01</sub>Ti<sub>0.99</sub>Se<sub>2</sub> the high-pressure resistivity curves show clearly the presence of the structural phase transition, and all three high-pressure curves show a maximum in -dlnρ/dp, in contrast to the ambient pressure curve for which the resistivity continues to rise rapidly below the transition. These results show the role of the distortion in achieving localisation through the reduction in the carrier concentration that it causes. It can be seen in figure 1 that the transition is pushed to lower temperatures under pressure at a rate similar to the value of 1.2 K kbar<sup>-1</sup> observed in pure TiSe<sub>2</sub> (Friend et al 1982).

<figure><img src="image_2.png" /><figcaption>Figure 2. Resistivity versus temperature for V<sub>0.03</sub>Ti<sub>0.97</sub>Se<sub>2</sub> at ambient pressure and at 15 kbar.</figcaption></figure>

Two effects may be contributing to the suppression of carrier localisation under pressure. Firstly, the increase in p-d band overlap with pressure directly increases the carrier concentration. Friend *et al* (1982) estimate that the p-d band overlap is increased at a rate of ~10 meV kbar<sup>-1</sup> in TiSe<sub>2</sub> and that the room-temperature rate of increase in carrier concentration dln/dp is of the order of 1.5 × 10<sup>19</sup> cm<sup>-3</sup> kbar<sup>-1</sup>. At low temperatures, below the distortion, the increase in carrier concentration is even more rapid, with an increase in conductivity at 4.2 K by a factor of over 50 between ambient pressure and 15 kbar. The Anderson (1958) criterion for localisation in the presence of a random potential of magnitude V<sub>0</sub> requires that the ratio of V<sub>0</sub> to the effective bandwidth B exceeds a critical value of order unity. The effective bandwidth for TiSe<sub>2</sub> will scale with the density of carriers present, and localisation is thus expected to become more difficult under pressure. Secondly, it is possible that the electrons localised on the V ions may become delocalised under pressure, and increase the carrier concentration further. This may come about, either through improved screening of the electron-electron interaction as the carrier concentration is increased, or through the decrease in metal-ion separation under pressure, which would increase the overlap of adjacent d orbitals, and favour band formation. Di Salvo and Waszczak (1978) have suggested that the larger value of the in-plane cell parameter in TiSe<sub>2</sub> of 3.54 Å compared to the value of 3.35 Å in metallic VSe<sub>2</sub> is an important factor in the formation of local moments on the substitutionally doped V in TiSe<sub>2</sub>. However, using the value for the in-plane compressibility measured for 2H-NbS<sub>2</sub> by Jones *et al* (1972) of 3.5 × 10<sup>-4</sup> kbar<sup>-1</sup>, the reduction in a axis in 15 kbar of ~0.2 Å is small compared to the difference between TiSe<sub>2</sub> and VSe<sub>2</sub>. Hydrate intercalation of V-doped TiSe<sub>2</sub>, in which there is a large increase in band filling and
carrier concentration, also has the effect of suppressing the low-temperature localisation and restoring metallic behaviour (Sarma *et al* 1982).

As seen in figure 1, under pressure the low-temperature conductivity passes through the expected value of the Mott minimum metallic conductivity $\sigma_{min}$ (Mott and Davis 1979) which for two-dimensional conduction has a value of ~300 ($\Omega$ cm$^{-1}$) for layer structure materials of this type (Di Salvo and Graebner 1977); the value of $\sigma_{min}$ for three-dimensional conduction is expected to be similar. Whilst conduction in d-band systems such as 1T-TaS$_2$ is two-dimensional, with estimates for the anisotropy in conductivity of 500 (Hambourger and Di Salvo 1980), conductivity in V-doped TiSe$_2$ may be three-dimensional, due to the presence of $p_z$ band holes, and Di Salvo *et al* (1976) report a very low value for the anisotropy in pure TiSe$_2$ of 2.5.

Since pressure is a convenient means of varying the strength of localisation in a continuous way, and in V$_{0.01}$Ti$_{0.99}$Se$_2$ moves the low-temperature conductivity through $\sigma_{min}$ in the pressure range up to 15 kbar, further experiments to lower temperatures may provide a test for current ideas of the sharpness of the metal-insulator transition at $\sigma_{min}$ (Abrahams *et al* 1979).

We thank Drs F J Di Salvo and F Lévy for the crystals used in this work.

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