Failure of the Wiedemann-Franz Law in Mesoscopic Conductors

TL;DR

This paper investigates how mesoscopic fluctuations cause deviations from the Wiedemann-Franz law in small conductors, revealing sample-specific corrections and flux-dependent oscillations at different temperature regimes.

Contribution

It demonstrates the temperature-dependent breakdown of the Wiedemann-Franz law in mesoscopic systems and highlights flux-periodic oscillations in ring geometries.

Findings

WF law holds at very low temperatures for each sample

Sample-specific corrections of order 1/g appear at intermediate temperatures

Flux-dependent oscillations in Lorenz number are observed in ring geometries

Abstract

We study the effect of mesoscopic fluctuations on the validity of the Wiedemann--Franz (WF) law for quasi-one-dimensional metal wires and open quantum dots. At temperatures much less than the generalized Thouless energy, E_c, the WF law is satisfied for each specific sample but as the temperature is raised through E_c a sample-specific correction to the WF law of order 1/g appears (g is the dimensionless conductance) and then tends to zero again at high temperatures. The mesoscopic violation of the Weidemann-Franz law is even more pronounced in a ring geometry, for which Lorenz number exhibits h/e flux-periodic Aharonov-Bohm oscillations.