Disorder and magnetic transport in tilted Weyl semimetals

We investigate the effect of disorder on the Landau levels (LLs) in tilted three dimensional Weyl semimetals (WSMs) when a magnetic field is present. Based on the minimum lattice model and by using the exact diagonalization and Kubo's formula, we numerically calculate the Hall conductivity and the density of states (DOS), from which several striking signatures are found to distinguish type-I WSMs from type-II WSMs: the first is the response of the Hall conductivity to the Fermi energy around the band center in clean limit, the second is the performance of the Hall conductivity to disorder, where in type-I WSMs, the robustness of the low-energy LLs is broken successively from the higher LLs to the lower ones and can be understood with the sink down picture, and the third is the behavior of the DOS at zero energy to disorder. The implications of our results are discussed.