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Band functions in the presence of magnetic steps

Hislop, P. D.; Popoff, N.; Raymond, N. and Persson Sundqvist, Mikael LU (2016) In Mathematical Models and Methods in Applied Sciences 26(1). p.161-161
Abstract
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
band functions, edge currents, Magnetic Schrodinger operators
in
Mathematical Models and Methods in Applied Sciences
volume
26
issue
1
pages
161 - 161
publisher
World Scientific
external identifiers
  • wos:000364233000005
  • scopus:84947019389
ISSN
1793-6314
DOI
10.1142/S0218202516500056
language
English
LU publication?
yes
id
e78970c5-6052-4352-bdde-c32ac81baf35 (old id 8386464)
date added to LUP
2015-12-22 08:15:34
date last changed
2017-01-01 06:00:54
@article{e78970c5-6052-4352-bdde-c32ac81baf35,
  abstract     = {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.},
  author       = {Hislop, P. D. and Popoff, N. and Raymond, N. and Persson Sundqvist, Mikael},
  issn         = {1793-6314},
  keyword      = {band functions,edge currents,Magnetic Schrodinger operators},
  language     = {eng},
  number       = {1},
  pages        = {161--161},
  publisher    = {World Scientific},
  series       = {Mathematical Models and Methods in Applied Sciences},
  title        = {Band functions in the presence of magnetic steps},
  url          = {http://dx.doi.org/10.1142/S0218202516500056},
  volume       = {26},
  year         = {2016},
}