Wiedemann-Franz law in scattering theory revisited

TL;DR

This paper revisits the Wiedemann-Franz law in noninteracting quantum systems with vanishing zero-energy transmission, identifying a universal Lorenz ratio of 21/5 and challenging the interpretation of WF law violations.

Contribution

It introduces a universal upper bound of 21/5 for the Lorenz ratio in weakly energy-dependent scattering systems with zero transmission, and discusses experimental setups to observe this ratio.

Findings

Universal Lorenz ratio of 21/5 identified

Violation of WF law does not imply non-Fermi-liquid behavior

Experimental realizations suggested for observing the Lorenz ratio

Abstract

The violation of Wiedemann-Franz (WF) law has been widely discussed in quantum transport experiments as an indication of deviation from Fermi-liquid behavior. The conventional form of WF law is only concerned with the transmission function at Fermi-level which, however, vanishes in many practical situations. We reinvestigate the WF law in noninteracting quantum systems with vanishing zero energy transmission and report a universal number $21/5$ as an upper bound of Lorenz ratio $\mathscr{R}$ in weakly energy-dependent scattering theory. We provide different experimental realizations for the observation of $\mathscr{R}=21/5$ namely the transport setups with graphene, the multi-level quantum dot and double quantum dot. The reported universal Lorenz ratio paves an efficient way of experimentally obtaining the information about the associated quantum interferences in the system. Our work also provides enough evidence which concludes that the violation of WF law does not necessarily imply the non-Fermi-liquid nature of underlying transport processes; equally, the Fermi-liquid transport characteristics cannot be concluded by an observed validation of WF law.