Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law

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 $g\le 1$) 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.

8 pages, 5 figures