Low Temperature Behavior of the Thermopower in Disordered Systems near the Anderson Transition

TL;DR

This study analyzes the low-temperature thermopower in disordered systems near the Anderson transition, resolving previous contradictions by numerically demonstrating that thermopower does not diverge as the transition is approached.

Contribution

It provides a numerical calculation of thermopower near the Anderson transition, clarifying its behavior and resolving conflicting prior claims.

Findings

Thermopower does not diverge near the Anderson transition.

Numerical methods confirm the constant or finite behavior of S at low T.

The approach uses the Anderson model and density of states calculations.

Abstract

We investigate the behavior of the thermoelectric power [S] in disordered systems close to the Anderson-type metal-insulator transition [MIT] at low temperatures. In the literature, we find contradictory results for S. It is either argued to diverge or to remain a constant as the MIT is approached. To resolve this dilemma, we calculate the number density of electrons at the MIT in disordered systems using an averaged density of states obtained by diagonalizing the three-dimensional Anderson model of localization. From the number density we obtain the temperature dependence of the chemical potential necessary to solve for S. Without any additional approximation, we use the Chester-Thellung-Kubo-Greenwood formulation and numerically obtain the behavior of S at low T as the Anderson transition is approached from the metallic side. We show that indeed S does not diverge.