Heat-bath approach to anomalous thermal transport: effects of inelastic scattering

TL;DR

This paper investigates how inelastic scattering influences anomalous charge and heat transport in metallic systems at finite temperatures, revealing non-universal behavior of the Wiedemann-Franz ratio due to Berry curvature effects.

Contribution

The study introduces a Caldeira-Leggett reservoir approach to incorporate inelastic dissipation in anomalous transport calculations, clarifying their impact on transport coefficients.

Findings

Wiedemann-Franz ratio is non-universal at finite temperatures.

Inelastic scattering causes the ratio to either increase or decrease with temperature.

Thermoelectric response ratio remains more universal at low temperatures.

Abstract

We present results for the entire set of anomalous charge and heat transport coefficients for metallic systems in the presence of a finite-temperature heat bath. In realistic physical systems this necessitates the inclusion of inelastic dissipation mechanisms; relatively little is known theoretically about their effects on anomalous transport. Here we demonstrate how these dissipative processes are strongly intertwined with Berry-curvature physics. Our calculations are made possible by the introduction of a Caldeira-Leggett reservoir which allows us to avoid the sometimes-problematic device of the pseudogravitational potential. Using our formulas, we focus on the finite-temperature behavior of the important anomalous Wiedemann-Franz ratio. Despite previous expectations, this ratio is found to be non-universal as it can exhibit either an upturn or a downturn as temperature increases away from zero. We emphasize that this derives from a \textit{competition} between Berry curvatures having different signs in different regions of the Brillouin zone. We point to experimental support for these observations and for the behavior of an alternative ratio involving a thermoelectric response which, by contrast, appears to be more universal at low temperatures. Our work paves the way for future theory and experiment, demonstrating how inelastic scattering at non-zero temperature affects the behavior of all anomalous transport coefficients.