An exactly solvable model of the disordered two-dimensional electron gas in a strong magnetic field

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Abstract
The authors examine a model of the disordered, non-iterating two-dimensional electron gas in a strong, perpendicular magnetic field, in which the Fermi energy is supposed to lie in the nth Landau level, for large n. The model is found to be exactly solvable in the limit n to infinity due to the vanishing of quantum interference between scattered wave packets. Three choices of random potential are examined: gaussian white noise; a uniform spatial distribution of zero-range scattering centres of fixed strength and with a lorentzian distribution of strengths. In all cases, all eigenstates are extended. Although the absence of quantum interference suppresses localisation, all the potentials lead to modulations in electron mobility across an impurity band and variations in the conductivity tensor with electron density which are reminiscent of the quantum Hall effect.