Violation of the Wiedemann-Franz law in clean graphene layers

TL;DR

This paper investigates how the Wiedemann-Franz law is violated in ultra-clean graphene layers due to electron-electron interactions affecting thermal and electrical conductivities differently, especially at low temperatures.

Contribution

It provides a detailed analysis of the density and temperature dependence of the thermal current relaxation time in doped graphene, revealing a specific ratio to quasiparticle decay rate.

Findings

At low temperature, the thermal current relaxation rate is 8/5 of the quasiparticle decay rate.

The many-body renormalization of the thermal Drude weight matches that of the Fermi velocity.

The study highlights significant deviations from the Wiedemann-Franz law in clean graphene layers.

Abstract

The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultra-clean conductors, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor $1+\tau/\tau_{\rm th}^{\rm ee}$, where $1/\tau$ is the momentum relaxation rate, and $1/\tau_{\rm th}^{\rm ee}$ is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of $1/\tau_{\rm th}^{\rm ee}$ in the important case of doped, clean single layers of graphene, which exhibit record-high thermal conductivities. We show that at low temperature $1/\tau_{\rm th}^{\rm ee}$ is $8/5$ of the quasiparticle decay rate. We also show that the many-body renormalization of the thermal Drude weight coincides with that of the Fermi velocity.