The axial anomaly in chiral tilted Weyl semimetals

The axial anomaly is investigated based on Fujikawa's method for chiral tilted Weyl semimetals, in which the Weyl cones with different chiralities tilt to opposite directions. When the electric field (EF) is parallel to the magnetic field (MF), the axial anomaly contributed by electromagnetic fields along tilt direction is reduced less than that along other directions. This results in that the associated effects, such as anomalous Hall effect, chiral magnetic effect and negative magnetoresistivity, are suppressed anisotropically. More interestingly, when the EF is perpendicular to MF, the axial anomaly has a new contribution from the mixed product of tilt vector, EF and MF, which is asymmetry under reversing tilt direction (electron-hole asymmetry) and leads to a current between Dirac cones with different tilt directions and novel magnetoresistivity (MR). Specifically, this contribution can change the properties of MR in some experimental establishments and makes trivial components of MR in un-tilted Weyl semimetal develop non-trivial properties. These changes are consistent with the MR phenomena observed in experiments, such as gate-tunable negative longitudinal MR, Hall MR, extremely large and non-saturating MR.