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

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.Screening is treated in the random-phase approximation by retaining the bubble diagrams, and the polarizability is obtained by solving the vertex function within the ladder approximation (which is consistent with the self-energy being treated in the single-site approximation). The resultant level broadening and the electronic density of states cannot easily be characterized by a single parameter, such as the zero-field mobility, which uniquely characterizes the usual short-range approximation extensively used in the literature. We find that the density of states calculated from this nonlinear, self-consistent screening theory is, in general, much smoother and flatter and the Landau-level broadening much larger than that implied in the short-range approximation. The density of states depends on the actual impurity distribution (and, not just on the mobility) in the system and the level broadening and screening are the oscillatory function of the chemical potential. We conclude that in many experimental situations the short-range approximation is even qualitatively wrong.We give detailed numerical results for the density of states and level broadening, and apply the theory to the calculation of thermodynamic quantities, such as electronic specific heat and magnetic susceptibility. Excellent qualitative and semiquantitative agreement with available experimental results is found.