Robustness of Landau levels of Dirac system in disorder

We study the disorder effect on Landau levels in gapped graphene and in transition metal dichalcogenides (TMDs). As a virtue of chiral structure, the lowest Landau in Dirac Hamiltonians is robust against long-range disorder that preserves chiral symmetry, including long-range correlated random hopping and fluctuating magnetic field. We investigate how much of this robustness is inherited by TMD monolayers by looking at a disordered three-band tight-binding model under a magnetic field. The implications for the physics of twisted bilayer TMDs are discussed.