Thermoelectric Effect of Correlated Metals - Band Structure Effects and the Breakdown of Mott's Formula

TL;DR

This paper investigates the thermoelectric properties of two-dimensional correlated metals, revealing limitations of Mott's formula under strong electron-electron interactions and highlighting the impact of band structure and Lifshitz transitions.

Contribution

It provides a detailed numerical analysis of thermoelectric effects considering full collision integrals, showing the breakdown of Mott's formula in correlated metals.

Findings

Mott's formula fails in the presence of strong electron-electron scattering.

Seebeck coefficient exhibits unusual temperature dependence near Lifshitz transitions.

Transport features near quantum critical points are mirrored in thermoelectric behavior.

Abstract

We study the thermoelectric effect of two-dimensional metals on a square lattice within semiclassical Boltzmann transport theory with particular focus on electron-electron scattering. We compute the electrical conductivity and the Seebeck coefficient as a function of band filling and temperature for generically chosen hopping parameters in a two-dimensional tight-binding model. The Boltzmann equation is solved numerically after computing the full collision integral, taking the angular and radial degrees of freedom into account. These degrees of freedom of the collision integral, neglected in the standard single-relaxation-time approximation, play an important role if the transport coefficients show unconventional features. Within our detailed numerical simulation, we show that the widely used Mott formula to compute the Seebeck effect is not sufficient to describe the thermoelectric effect in the presence of strong electron-electron scattering. Furthermore, we study the Seebeck coefficient and its temperature dependence in the vicinity of a Lifshitz transition and demonstrate that it shows remarkable parallels to transport features near a quantum critical point.