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The chiral magnetic effect is a one of the exotic bulk transport propertiesof the Weyl semimetals. Because of the Nielsen-Ninomiya "no-go theorem", thetotal chiral magnetic current is absent in the equilibrium state. One of themechanisms for generating this current is the chiral anomaly. This phenomenonis the anomalous nonconservation of chiral charge for massless relativisticparticles. It can be realized by parallel magnetic and electric fields, and itleads to such new transport phenomenon as the negative longitudinalmagnetoresistance. Using a simple theory (we consider both linearized andlattice model), we have shown, that in Weyl metals with tilted dispersionanother mechanism of the chiral magnetic current is possible. It is notassociated with the chiral anomaly. The new transport mechanism is based on therelativistic effect of electric field on Landau levels. This effect is that anelectric field changes the distance between the Landau levels, and also changesthe effective velocity along magnetic field. At presence of a tilt in thespectrum, this velocity renormalization is differ for different Weyl points.This leads to a non-zero resulting drift velocity. As a consequence, anelectrical current arises along the magnetic field. The induced by thismechanism the electric current is proportional to the pseudoscalar product ofthe fields and directed along the magnetic field, that differs it from the Hallcurrent. At the same time, the conductivity corresponding to this transportmechanism does not depend on the scattering time like the Hall conductivity.Thus, we have proposed a new anomalous transport mechanism in the Weylsemimetal, which is not associated with the chiral anomaly.

Relativistic Mechanism of Chiral Magnetic Current in Weyl Semimetals with Tilted Dispersion