Density of states of a two-dimensional electron gas in a perpendicular magneticfield and a random field of arbitrary correlation

Abstract

A theory is given of the density of states (DOS) of a two-dimensional electron gassubjected to a uniform perpendicular magnetic field and any random field,adequately taking into account the realistic correlation function of the latter. Fora random field of any long-range correlation, a semiclassical non-perturbativepath-integral approach is developed and provides an analytic solution for theLandau level DOS. For a random field of any arbitrary correlation, acomputational approach is developed. In the case when the random field issmooth enough, the analytic solution is found to be in very good agreement withthe computational solution. It is proved that there is not necessarily a universalform for the Landau level DOS. The classical DOS exhibits a symmetric Gaussianform whose width depends merely on the rms potential of the randomfield. The quantum correction results in an asymmetric non-GaussianDOS whose width depends not only on the rms potential and correlationlength of the random field, but the applied magnetic field as well. Thedeviation of the DOS from the Gaussian form is increased when reducing thecorrelation length and/or weakening the magnetic field. Applied to amodulation-doped quantum well, the theory turns out to be able to give aquantitative explanation of experimental data with no fitting parameters.