Anomalous Lorenz number in massive and tilted Dirac systems

TL;DR

This paper analytically investigates how the Lorenz number deviates from its classical value in massive and tilted Dirac materials, influenced by Berry curvature, tilt, and anisotropy, with implications for thermoelectric device optimization.

Contribution

It provides an analytical framework for understanding anomalous Lorenz number deviations in Dirac systems, incorporating effects of tilt, anisotropy, and Berry curvature.

Findings

Deviations in Lorenz number are linked to kinetic transport differences at high temperatures.

Tilt and anisotropy significantly influence the anomalous Lorenz number.

The study offers insights for tuning thermoelectric properties via external stimuli.

Abstract

We analytically calculate the anomalous transverse electric and thermal currents in massive and tilted Dirac systems, using $ \beta $-borophene as a representative material, and report on conditions under which the corresponding Lorenz number $\left(\mathcal{L}_{an}\right)$ deviates from its classically accepted value $\left(\mathcal{L}_{0}\right)$. The deviations in the high-temperature regime are shown to be an outcome of the quantitative difference in the respective kinetic transport expressions for electric $\left(\sigma\right)$ and thermal $\left(\kappa\right)$ conductivity, and are further weighted through a convolution integral with a non-linearly energy-dependent Berry curvature that naturally arises in a Dirac material. In addition, the tilt and anisotropy of the Dirac system that are amenable to change via external stimulus are found to quantitatively influence $ \mathcal{L}_{an} $. The reported deviations from $\mathcal{L}_{0} $ hold practical utility inasmuch as they allow an independent tuning of $\sigma $ and $ \kappa $, useful in optimizing the output of thermoelectric devices.