Anharmonicity and asymmetry of Landau levels for a disordered two-dimensional electron gas

We calculate the density of states of a two-dimensional electron gas located at the interface of a strongly disordered $\mathrm{Ga}\mathrm{Al}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterojunction. The disorder potential is created by two delta doped layers. The first layer includes the parent donors which provides the well with electrons and creates a smooth disorder potential. The second layer is doped with either acceptor or donor impurities, and is located inside the well, thus creating a strongly disordered potential. We calculate the density of states in the presence of a magnetic field of arbitrary strength by taking into account all perturbative terms in the fifth Klauder's approximation. We find an anharmonic spectrum, strongly asymmetric, for the Landau level density of states. At low field, the attractive potential creates the well-known band tails or impurity bands. At higher field, we show that impurity bands are also created by repulsive potentials. We discuss the consequences of the anharmonicity and asymmetry on physical properties in the quantum Hall effect regime.