Electron transport at the Anderson transition

The low-temperature behavior of transport properties across an Anderson-type metal-insulator transition is considered. It is shown that previous discussions are flawed; in particular, we demonstrate that the thermopower S is not divergent as the mobility edge ${\mathit{E}}_{\mathit{c}}$ is approached from the metallic side. At ${\mathit{E}}_{\mathit{c}}$, S achieves a temperature-independent value, determined solely by the conductivity index ν. Furthermore, far from being universal in the metallic phase, the Lorentz number changes as the mobility edge is approached and, in addition, depends on ν. We also prove that, contrary to previous assertions, the thermal conductivity varies like ${\mathit{T}}^{\nu +1\mathrm{}}$ as T→0.