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Band functions in the presence of magnetic steps

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Author

Summary, in English

We complete the analysis of the band functions for two-dimensional magnetic Schrodinger operators with piecewise constant magnetic fields. The discontinuity of the magnetic field can create edge currents that flow along the discontinuity, which have been described by physicists. Properties of these edge currents are directly related to the behavior of the band functions. The effective potential of the fiber operator is an asymmetric double well (eventually degenerated) and the analysis of the splitting of the bands incorporates the asymmetry. If the magnetic field vanishes, the reduced operator has essential spectrum and we provide an explicit description of the band functions located below the essential spectrum. For non-degenerate magnetic steps, we provide an asymptotic expansion of the band functions at infinity. We prove that when the ratio of the two magnetic fields is rational, a splitting of the band functions occurs and has a natural order, predicted by numerical computations.

Publishing year

2016

Language

English

Pages

161-161

Publication/Series

Mathematical Models and Methods in Applied Sciences

Volume

26

Issue

1

Document type

Journal article

Publisher

World Scientific Publishing

Topic

  • Mathematical Analysis

Keywords

  • band functions
  • edge currents
  • Magnetic Schrodinger operators

Status

Published

ISBN/ISSN/Other

  • ISSN: 1793-6314