Magnetic field and electron states in two-dimensional disordered systems

Abstract

The density of states and the exponential decay of a two-dimensional disordered system subject to a magnetic field are calculated using a new iterative technique. The influence of the boundary conditions is investigated. For cylinder geometry states in the centres of the magnetic sub-bands are found that extend throughout the whole system. For strip geometry the existence of disorder-independent edge states is shown. These extend along the whole length of the boundary of the sample. The implications of the results for the explanation of the quantum Hall effect are discussed.