Electron density of states and localization of two-dimensional disordered systems in quantized magnetic fields

Abstract

We study numerically non-interacting electrons moving on a two-dimensional lattice with a uniform magnetic field and a random site potential. The electron localization and the density of states are investigated by using the method of transfer-matrices and by the direct diagonalization technique. For numerical simulations the Ando model with the diagonal disorder is used. The first preliminary data have been obtained for different sizes of the system and various values of the magnetic field. The localization length exhibits Shubnikov-de-Haas oscillations. The density of states shows several Landau bands separated by the energy gaps. With increasing the disorder the Landau bands becomes broader and overlap with each other. The application of the obtained results to the integer quantum Hall effect is discussed.