Fate of the Wiedemann-Franz law near quantum critical points of electron systems in solids

TL;DR

This paper explores how the Wiedemann-Franz law can be violated near quantum critical points in strongly correlated electron systems, due to collective modes and flat band formation affecting thermal and electrical conductivities.

Contribution

It introduces two mechanisms for WF law violation near a topological quantum critical point, one involving zero-sound modes and the other flat band formation.

Findings

Transverse zero-sound mode enhances thermal conductivity on the FL side.

Flat band formation reduces the Lorenz number on the NFL side.

Two distinct violation mechanisms are identified near TQCP.

Abstract

We introduce and analyze two different scenarios for violation of the Wiedemann-Franz law in strongly correlated electron systems of solids, close to a topological quantum critical point (TQCP) where the density of states $N(0)$ diverges. The first, applicable to the Fermi-liquid (FL) side of the TQCP, involves a transverse zero-sound collective mode that opens a new channel for the thermal conductivity, thereby enhancing the Lorenz number $L(0)$ relative to the value $L_0=\pi^2k^2_B/3e^2$ dictated by conventional FL theory. The second mechanism for violation of the WF law, relevant to the non-Fermi-liquid (NFL) side of the TQCP, involves the formation of a flat band and leads instead to a reduction of the Lorenz number.