Shape of the Landau subbands in disordered graphene

The question of why different experiments obtain different shapes of Landau subbands of two-dimensional electron gases (2DEG's) is investigated. In particular, we consider disordered graphene within the tight-binding formulation in a high magnetic field and in the presence of impurity potentials of a finite interaction range. It is found that the shape of the total density of states (DOS) of Landau subbands is well described by a Gaussian function, while the shape of the local density of states (LDOS) can be fitted to either a simple Lorentzian function or a sum of several Lorentzian functions. This finding explains well why the experiments that measure the DOS of a Landau subband appear to be Gaussian, and those experiments that are sensitive to the LDOS can only be fitted well by Lorentzian functions. Thus, our results provide a natural explanation to this long-standing puzzle involving 2DEG's in the quantum Hall regime.