  The chiral magnetic effect is a one of the exotic bulk transport properties
of the Weyl semimetals. Because of the Nielsen-Ninomiya "no-go theorem", the
total chiral magnetic current is absent in the equilibrium state. One of the
mechanisms for generating this current is the chiral anomaly. This phenomenon
is the anomalous nonconservation of chiral charge for massless relativistic
particles. It can be realized by parallel magnetic and electric fields, and it
leads to such new transport phenomenon as the negative longitudinal
magnetoresistance. Using a simple theory (we consider both linearized and
lattice model), we have shown, that in Weyl metals with tilted dispersion
another mechanism of the chiral magnetic current is possible. It is not
associated with the chiral anomaly. The new transport mechanism is based on the
relativistic effect of electric field on Landau levels. This effect is that an
electric field changes the distance between the Landau levels, and also changes
the effective velocity along magnetic field. At presence of a tilt in the
spectrum, this velocity renormalization is differ for different Weyl points.
This leads to a non-zero resulting drift velocity. As a consequence, an
electrical current arises along the magnetic field. The induced by this
mechanism the electric current is proportional to the pseudoscalar product of
the fields and directed along the magnetic field, that differs it from the Hall
current. At the same time, the conductivity corresponding to this transport
mechanism does not depend on the scattering time like the Hall conductivity.
Thus, we have proposed a new anomalous transport mechanism in the Weyl
semimetal, which is not associated with the chiral anomaly.
