Pseudogap of liquidTl2Te

Analysis of experimental curves for the electrical conductivity $\sigma$ and thermopower $S$ of ${\mathrm{Tl}}_x{\mathrm{Te}}_{1-x}$ alloys near the composition ${\mathrm{Tl}}_2$Te has yielded a quantitative description of the pseudogap. A model expressed in terms of two bands with a negative temperature coefficient for the band gap has been fitted with parameters which yield very good agreement with the experimental curves. The theoretical expressions for $S$ and $\sigma$ are based on the diffusive mechanism for transport, according to which the conductivity at a given energy $\sigma \mathrm{}\left(E\right)\mathrm{}$ is proportional to the square of the density of states $N\left(E\right)\mathrm{}$. The effect of the mobility shoulder is to cut off $\sigma \mathrm{}\left(E\right)\mathrm{}$ at the mobility edges. For the conduction band, it is found that the density of states $N_c\mathrm{}\left(E\right)\mathrm{}$ is parabolic. The mobility edge $E_{c1}$ is within $\mathrm{kT}$ of the band edge $E_{c0}$, and is therefore not experimentally discernible. For the valence band, the results are more ambiguous. A parabolic density of states $N_v\mathrm{}\left(E\right)\mathrm{}$ yields fairly accurate results, and we deduce a value ∼0.20 eV for the distance of the mobility edge $E_{v1}$ from the band edge $E_{v0}$, but there are some uncertainties associated with both of these results. At $T>\mathrm{}770\mathrm{}$ °K, the band gap becomes negative. In accordance with Mott's observation that localized and nonlocalized states cannot overlap in energy, our model takes $\sigma \mathrm{}\left(E\right)\mathrm{}\propto {\left[N_c\mathrm{}\right(E)+N_v\mathrm{}(E\left)\right]}^2$, and localized valence-band states become conducting when their energies rise above the conduction-band mobility edge.