  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.
