Band functions in the presence of magnetic steps
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8386464
- author
- Hislop, P. D. ; Popoff, N. ; Raymond, N. and Persson Sundqvist, Mikael LU
- organization
- publishing date
- 2016
- 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 Publishing
- 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
- 2016-04-01 14:01:56
- date last changed
- 2022-03-21 21:54:24
@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}}, keywords = {{band functions; edge currents; Magnetic Schrodinger operators}}, language = {{eng}}, number = {{1}}, pages = {{161--161}}, publisher = {{World Scientific Publishing}}, 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}}, doi = {{10.1142/S0218202516500056}}, volume = {{26}}, year = {{2016}}, }