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

• Received 11 March 2014
• Revised 29 August 2014

DOI:https://doi.org/10.1103/PhysRevB.90.121108