Quantum Kinetic Theory of Thermoelectric and Thermal Transport in a Magnetic Field

TL;DR

This paper develops a comprehensive quantum kinetic theory to analyze thermoelectric and thermal transport in magnetic fields, incorporating Berry curvatures, disorder, and temperature gradients, with applications to Weyl semimetals.

Contribution

It introduces a novel quantum kinetic framework that systematically includes temperature gradients, Berry curvatures, and disorder to compute transport coefficients at arbitrary field strengths.

Findings

Derived a general expression for electron valley pumping rate in temperature gradients and magnetic fields.

Established a relation analogous to the Mott relation between pumping rates due to temperature gradients and electric fields.

Showed the violation of the Wiedemann-Franz law in chiral-anomaly induced thermal conductivity in Weyl semimetals.

Abstract

We present a general quantum kinetic theory that accounts for the interplay between a temperature gradient, momentum-space Berry curvatures of Bloch electrons, and Bloch-state scattering. Using a theory that incorporates the presence of a temperature gradient by introducing a "thermal vector potential", we derive a quantum kinetic equation for Bloch electrons in the presence of disorder and a temperature gradient. Taking also into account the presence of electric and magnetic fields, the quantum kinetic equation we derive makes it possible to compute transport coefficients at arbitrary orders of electric-field $\vec{E}$, magnetic-field $\vec{B}$, and temperature-gradient $\nabla T$ strengths $|\vec{E}|^a |\vec{B}|^b |\nabla T|^c$. Our theory enables a systematic calculation of magnetothermoelectric and magnetothermal conductivities of systems with momentum-space Berry curvatures. As an illustration, we derive from a general microscopic electron model a general expression for the rate of pumping of electrons between valleys in parallel temperature gradient and magnetic field. From this expression we find a relation, which is analogous to the Mott relation, between the rate of pumping due to a temperature gradient and that due to an electric field. We also apply our theory to a two-band model for Weyl semimetals to study thermoelectric and thermal transport in a magnetic field. We show that the Mott relation is satisfied in the chiral-anomaly induced thermoelectric conductivity, and that the Wiedemann-Franz law is violated in the chiral-anomaly induced thermal conductivity, which are both consistent with the results obtained by invoking semiclassical wave-packet dynamics.