Role of axion electrodynamics in Weyl metal: Violation of Wiedemann-Franz law

TL;DR

This paper investigates how axion electrodynamics causes the violation of the Wiedemann-Franz law in Weyl metals, revealing that anomalous currents differ and indicating a topologically non-Fermi-liquid state.

Contribution

It demonstrates that the Wiedemann-Franz law breakdown in Weyl metals arises from axion electrodynamics, providing a new hallmark of their topological nature.

Findings

B² enhancement observed in both LMEC and thermal conductivities

Wiedemann-Franz law is violated despite the presence of quasiparticles

Anomalous currents differ, indicating non-Fermi-liquid behavior

Abstract

Recently, enhancement of the longitudinal magneto-electrical conductivity (LMEC) has been observed in Bi$_{1-x}$Sb$_{x}$ around $x \sim 3\%$ under $\bm{E} \parallel \bm{B}$ ($\bm{E}$: external electric field and $\bm{B}$: external magnetic field) [Phys. Rev. Lett. {\bf 111}, 246603 (2013)], where an enhancement factor proportional to $B^{2}$ is suggested to result from the $\bm{E} \cdot \bm{B}$ term. In the present study, we show that this $B^{2}$ enhancement is not limited on the LMEC, where both the Seebeck and thermal conductivities in the longitudinal setup ($\bm{E} \parallel \bm{B}$) are predicted to show essentially the same enhancement proportional to $B^{2}$. In particular, the $B^{2}$ enhancement factor of the LMEC turns out to differ from that of the longitudinal thermal conductivity, responsible for breakdown of Wiedemann-Franz (WF) law, which means that anomalous currents flowing through the dissipationless channel differ from each other. Since the breakdown of the WF law appears in spite of the existence of electron quasiparticles, regarded to be a purely topological character (chiral anomaly), the Weyl metallic state cannot be identified with the Landau's Fermi-liquid fixed point. We propose the violation of the WF law as another hallmark of the Weyl metallic phase, which originates from axion electrodynamics.