Effect of Impurities on the Level Density of an Electron Gas in a Strong Magnetic Field

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Abstract
The effect of impurities on the level density of an electron gas in a strong magnetic field is investigated. An approximate closed set of equations is given for the one-particle Green's function of the electron gas assuming the random distribution of the impurities. The self-energy included is the sum of multiple scattering from each impurity where the true Green's function is used for the propagator. The set of equations is solved numerically in a self-consistent way for the level density. Discussions are given for the validity of various approximations proposed in the past for this system.