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On the extended nature of edge states of quantum Hall Hamiltonians. (English) Zbl 1004.81043
Summary: Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized near the boundary of a two-dimensional electron gas – so-called edge states – are studied. For finite samples it is shown that edge states with energy in an appropriate range between Landau levels remain extended along the boundary in the presence of a small amount of disorder, in the sense that they carry a non-zero chiral edge current. For a two-dimensional electron gas confined to a half-plane, or to a domain in the plane satisfying a certain geometric condition, the Mourre theory of positive commutators is applied to prove absolute continuity of the energy spectrum well in between Landau levels, corresponding to edge states.

MSC:
81V70 Many-body theory; quantum Hall effect
81Q99 General mathematical topics and methods in quantum theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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