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

Abstract

Recently, enhancement of the longitudinal magneto-electrical conductivity (LMEC) has been observed in Bi${}_{1-x}$Sb${}_x$ around $x\sim 3\%$ under $\mathbf{E}\parallel \mathbf{B}$ ($\mathbf{E}$: external electric field and $\mathbf{B}$: external magnetic field) [Phys. Rev. Lett. {\bf 111}, 246603 (2013)], where an enhancement factor proportional to $B^2$ is suggested to result from the $\mathbf{E}\cdot \mathbf{B}$ 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 ($\mathbf{E}\parallel \mathbf{B}$) 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.

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• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
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• Chiral anomalies induced transport in Weyl semimetals in quantizing magnetic field
• Large Violation of the Wiedemann Franz Law in Heusler, Ferromagnetic, Weyl Semimetal Co${}_2$MnAl
• Severe violation of the Wiedemann-Franz law in quantum oscillations of NbP
• Anomalous Hall effects beyond Berry magnetic fields in a Weyl metal phase
• Nonlocal transport phenomena in Weyl metals beyond the mesoscopic scale
• Interplay of the orbital magnetic moment and the chiral magnetic effect in Shubnikov-de Haas quantum oscillations