Wiedemann-Franz law in scattering theory revisited

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 $\mathcal{R}$ 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 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.

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Cited by in corpus (6)

• Wiedemann-Franz law for massless Dirac fermions with implications for graphene
• Generalized Wiedemann-Franz law in a two-site charge Kondo circuit: Lorenz ratio as a manifestation of the orthogonality catastrophe
• Coulomb blockade oscillations of heat conductance in the charge Kondo regime
• Transition between heavy-fermion strange metal and quantum spin liquid in a 4d-electron trimer lattice
• Universal relations between thermoelectrics and noise in mesoscopic transport across a tunnel junction
• Heat conductance oscillations in two weakly connected charge Kondo circuits