On edge states in semi-infinite quantum Hall systems

Details On edge states in semi-infinite quantum Hall systems On edge states in semi-infinite quantum Hall systems

1998-12-22

arxiv.org/abs/cond-mat/9812367v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

20 pages, no figures, plain TEX, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/32/10/015

We consider an electron in two dimensions submitted to a magnetic field and to the potential of impurities. We show that when the electron is confined to a half-space by a planar wall described by a smooth increasing potential, the total Hamiltonian necessarily has a continuous spectrum in some intervals in-between the Landau levels provided that both the amplitude and spatial variation of the impurity potential are sufficiently weak. The spatial decay of the impurity potential is not needed. In particular this proves the occurence of edge states in semi-infinite quantum Hall systems.

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