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Band functions in the presence of magnetic steps

In English

Författare

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.

Avdelning/ar

Publiceringsår

2016

Språk

Engelska

Sidor

161-161

Publikation/Tidskrift/Serie

Mathematical Models and Methods in Applied Sciences

Volym

26

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

World Scientific Publishing

Ämne

  • Mathematical Analysis

Nyckelord

  • band functions
  • edge currents
  • Magnetic Schrodinger operators

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 1793-6314