Nernst effect beyond the relaxation-time approximation

TL;DR

This paper investigates the Nernst effect in anisotropic materials, comparing exact Boltzmann solutions with approximations, revealing significant limitations of common methods especially in anisotropic regimes.

Contribution

It provides an exact solution for the Nernst effect with anisotropic dispersion and scattering, highlighting deficiencies in the relaxation-time approximation.

Findings

Relaxation-time approximation can incorrectly predict the sign of the Nernst coefficient.

Ziman's improvement fails to account for combined anisotropic effects.

Exact solutions reveal qualitative differences from approximate methods.

Abstract

Motivated by recent interest in the Nernst effect in cuprate superconductors, we calculate this magneto-thermo-electric effect for an arbitrary (anisotropic) quasiparticle dispersion relation and elastic scattering rate. The exact solution of the linearized Boltzmann equation is compared with the commonly used relaxation-time approximation. We find qualitative deficiencies of this approximation, to the extent that it can get the sign wrong of the Nernst coefficient. Ziman's improvement of the relaxation-time approximation, which becomes exact when the Fermi surface is isotropic, also cannot capture the combined effects of anisotropy in dispersion and scattering.