Low-temperature a.c. conductivity of vanadium dioxide crystals

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Abstract
The dielectric constant ε′(ω) and the a.c. conductivity σ(ω) of undoped and lightly doped (0·5% Al, 0·8% Ti, 0·5% W) crystals of vanadium dioxide (VO2) are reported for the temperature range 4·2–77 K and the frequency range 0·1–100 kHz. The 0·5% W-doped sample shows a strong dispersion in ε′(ω) and a frequency-independent σ(ω) above 60 K, similar to the reported behaviour of undoped, Ti- and Al-doped samples at much higher temperatures. The temperature dependence of both ε′(ω) and σ(ω) at a fixed frequency indicates that these parameters have a finite value at T→0 K, and below 20 K they can be expressed by a relation of the form (α + βT), where α and β are constants which are independent of temperature, but that depend on frequency. The a.c. conductivity can be expressed as σ(ω) = A(ω)s, where the slope ‘s’ at 4·2 K is between 1 and 0·8 for all the samples. s is found to decrease with increasing temperature. This decrease of s with temperature and the finite value of α(ω) at T→0 K are consistent with the theoretical model based on hopping over the barrier; however, the validity of this HOB model at 4·2 K leads to an unrealistic value of the bandwidth (< 1 meV). The tunnelling model, which takes into consideration electron-electron interactions, seems more appropriate for the system but fails to give quantitative agreement with the experimental data.

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