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 \ensuremath{\nu}. Furthermore, far from being universal in the metallic phase, the Lorentz number changes as the mobility edge is approached and, in addition, depends on \ensuremath{\nu}. We also prove that, contrary to previous assertions, the thermal conductivity varies like ${\mathit{T}}^{\ensuremath{\nu}+1}$ as T\ensuremath{\rightarrow}0.