A comparison of magnetoconductivities between type-I and type-II Weyl semimetals

It is well known that Weyl semimetals (WSMs) are classified into two types of type-I and type-II depending on whether or not they have electron and hole pockets. Also, these WSMs have peculiar transport properties such as negative longitudinal magnetoresistance and planar Hall effect because of a chiral anomaly. In this paper, however, we show that the chiral anomaly can cause positive longitudinal magnetoresistance in type-II WSMs. Here, we investigate longitudinal and transverse magnetoconductivities of time reversal symmetry broken type-I and type-II WSMs using a tight-binding model. The model allows us to describe both types of type-I and type-II WSMs by tuning parameters, and it has two Weyl points that are separated along the k x-direction. The numerical calculations of these conductivities are performed using the Boltzmann equation including the Berry curvature. It is found that longitudinal magnetoconductivities in the x-direction can have both positive and negative values depending on the magnitude of the inclination of a Weyl cone. This is because the zeroth Landau energy-level becomes either a hole-like one or an electron-like one depending on the magnitude of the inclination of the Weyl cone in type-II WSMs. These results imply that we can make a high MR-ratio device using type-II WSMs by tuning the inclination of their cones if it is possible to change their energy bands by the application of electric field and so on.