On the extended nature of edge states of Quantum Hall Hamiltonians

Details On the extended nature of edge states of Quantum Hall Hamiltonians On the extended nature of edge states of Quantum Hall Hamiltonians

1999-03-08

arxiv.org/abs/math-ph/9903014v2

Physics

Mathematical Physics

45 pages, 7 figures, reference added

Scientific paper

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, 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.

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