Wiedemann-Franz law in scattering theory revisited

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 the 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 the Lorenz ratio $\mathcal{R}$ in weakly energy-dependent scattering theory. We provide different experimental realizations for the observation of $\mathcal{R}=21/5$, namely, the transport setups with graphene, the multilevel 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.