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

TL;DR

This paper investigates how disorder affects the zero-mode Landau levels in massless Dirac fermions, revealing that chiral symmetry preserves the sharpness of the n=0 Landau level even with uncorrelated disorder, especially without fermion doubling.

Contribution

It introduces a tight-binding model with complex transfer integral to control fermion doubling and analyzes the impact of disorder on Landau levels, highlighting the role of chiral symmetry.

Findings

Zero-mode Landau level remains sharp with chiral-symmetric disorder.

Fermion doubling influences the Landau level structure.

Chiral symmetry protects the n=0 Landau level from broadening.

Abstract

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