Chiral symmetry and fermion doubling in the zero-mode Landau levels of massless Dirac fermions with disorder

摘要

The effect of disorder on the Landau levels of massless Dirac fermions isexamined for the cases with and without the fermion doubling. To tune thedoubling a tight-binding model having a complex transfer integral is adopted toshift the energies of two Dirac cones, which is theoretically proposed earlierand realizable in cold atoms in an optical lattice. In the absence of thefermion doubling, the $n=0$ Landau level is shown to exhibit an anomaloussharpness even if the disorder is uncorrelated in space (i.e., large K-K'scattering). This anomaly occurs when the disorder respects the chiral symmetryof the Dirac cone.