UNIVERSAL SCALING OF STRONG-FIELD LOCALIZATION IN AN INTEGER QUANTUM HALL LIQUID

We study the Landau level localization and scaling properties of a dis ordered two-dimensional electron gas in the presence of a strong exter nal magnetic field. The impurities are treated as randomly distributed scattering centers with parametrized potentials. Using a transfer mat rix for a finite-width-strip geometry, we calculate the localization l ength as a function of system size and electron energy. The finite-siz e localization length is determined by calculating the Lyapunov expone nts of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau ban ds. The influence of varying the impurity concentration, the scatterin g potential range and its nature, and the Landau level index on the sc aling behavior and on the critical exponent is systematically investig ated. Particular emphasis is put on Studying the effects of finite ran ge of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure del ta-function disorder in the absence of any Landau level coupling gives rise to nonuniversal localization properties with the critical expone nts in the lowest two Landau levels being substantially different. inc lusion of a finite potential range and/or Landau level mixing may be e ssential in producing universality in the localization.