Thermal vector potential theory of transport induced by temperature gradient

TL;DR

This paper introduces a microscopic formalism using a thermal vector potential to accurately calculate thermal transport coefficients, avoiding unphysical divergences present in previous methods.

Contribution

It presents a novel formalism based on a thermal vector potential that correctly accounts for equilibrium currents and parallels electric transport theory.

Findings

Formalism is free from unphysical divergences.

Mathematical structure mirrors electric transport with energy replacement.

Thermal vector potential couples to energy current via minimal coupling.

Abstract

A microscopic formalism to calculate thermal transport coefficients is presented based on a thermal vector potential, whose time-derivative is related to a thermal force. The formalism is free from unphysical divergences reported to arise when Luttinger's formalism is applied naively, because the equilibrium (\textquoteleft diamagnetic\textquoteright) currents are treated consistently. The mathematical structure for thermal transport coefficients are shown to be identical with the electric ones if the electric charge is replaced by energy. The results indicates that the thermal vector potential couples to energy current via the minimal coupling.