  Electronic transport in Weyl semimetals is quite extraordinary due to the
topological property of the chiral anomaly generating the charge pumping
between two distant Weyl nodes with opposite chiralities under parallel
electric and magnetic fields. Here, we develop a full nonequilibrium quantum
transport theory of the chiral anomaly, based on the fact that the chiral
charge pumping is essentially nothing but the Bloch oscillation. Specifically,
by using the Keldysh nonequilibrium Green function method, it is shown that
there is a rich structure in the chiral anomaly transport, including the
negative magnetoresistance, the non-Ohmic behavior, the Esaki-Tsu peak, and
finally the resonant oscillation of the DC electric current as a function of
electric field, called the electric quantum oscillation. We argue that, going
beyond the usual behavior of linear response, the non-Ohmic behavior observed
in BiSb alloys can be regarded as a precursor to the occurrence of electric
quantum oscillation, which is both topologically and energetically protected in
Weyl semimetals.
