Density of states and thermodynamic properties of a two-dimensional electron gas in a strong external magnetic field

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Abstract
We develop a theory for the electronic density of states of a weakly disordered two-dimensional electron gas in the presence of a strong external magnetic field oriented normal to the electron layer. The disorder arises from randomly distributed charged impurity centers that interact with the electrons, in the absence of any screening, via the long-range Coulomb interaction. To mimic modulation doping in high-mobility heterostructures, the electron plane is assumed to be separated by a spacer layer from the impurity plane. The density of states is calculated using the self-consistent Born approximation for the electron-impurity scattering, retaining Landau-level coupling in the theory. The electron-impurity scattering potential is calculated in a nonlinear screening approximation where scattering and screening self-consistently determine each other. Thus, the level broadening determining the electron propagator in each Landau level is calculated by using the screened impurity potential in the self-consistent Born approximation, whereas the screened potential itself is calculated self-consistently by calculating the electron polarizability with use of the renormalized electron propagator.