Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law

TL;DR

This paper explores how fractional exclusion statistics influence quantum transport, revealing violations of the Wiedemann-Franz law and enhanced thermoelectric efficiency, with potential implications for thermoelectric material design.

Contribution

It introduces a duality relation for Haldane-Wu statistics and demonstrates significant transport anomalies, including Wiedemann-Franz law violations and thermoelectric improvements, based on statistical interaction parameter g.

Findings

Wiedemann-Franz law is violated for g>1 across broad temperatures.

Thermoelectric figure of merit ZT is enhanced for g>1.

Particle-hole symmetry breaking correlates with transport anomalies.

Abstract

Quantum transport anomalies in systems obeying Haldane-Wu fractional exclusion statistics, characterized by the statistical interactions parameter $g$ are investigated. We identify particle-hole symmetry breaking of the Haldane-Wu distribution function via its deviations of the maximum entropy ($\mathcal{S}_{g}^{max}$), evaluated at the chemical potential, from the value ${k_B} \ln 2$ (a value that holds only at the free fermion limit, $g=1$). A duality relation, $g\,\mathcal{S}_{g}^{max}=\mathcal{S}_{1/g}^{max}$, quantifying the degree of violation is obtained. This symmetry breaking manifests in transport phenomena as: significant violations of the Wiedemann-Franz law arising for $g>1$ (but remain absent for $g\leq 1$) across a broad temperature range. Moreover, the thermoelectric figure of merit $ZT$ is substantially enhanced for $g>1$ and suppressed for $g<1$, indicating new routes to optimize energy conversion. These results deepen the understanding of the interplay between equilibrium statistics and transport, suggesting avenues for engineering advanced thermoelectric materials.