Self-Consistent Treatment of Dynamical Diffusion Coefficient of Two Dimensional Random Electron System under Strong Magnetic Fields

Abstract

Diagramatic treatment for the density relaxation function is employed to determine the renormalized dynamical diffusion coefficient D(ω) of two dimensional random electron system under quantizing magnetic fields; for simplicity, the case where the Fermi energy lies within the lowest Landau subband is considered. The resulting self-consistent equation shows that D(0) does not vanish only when the real part of the retarded Green’s function at the Fermi level is zero. The quantities, such as ReD(ω), ImD(ω) and the localization length, are calculated numerically by changing the Fermi energy within the lowest subband. The measure of the number of extended states per unit area is zero, but extended states do exist, which does not contradict with the observation of the quantized Hall effect.