Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps
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parzygnat-9.pdf
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Main article
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Author(s)
Johnson, Steven G.
Avniel, Yehuda B.
Lee, Karen Ka Yan
Parzygnat, Arthur J.
Date Issued
April 2010
Journal
Physical Review B
Publisher
American Physical Society
Citation
Parzygnat, Arthur et al. “Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps.” Physical Review B 81.15 (2010): 155324. © 2010 The American Physical Society
Version
Author's final manuscript
Abstract
We prove, via an elementary variational method, one-dimensional (1D) and two-dimensional (2D) localization within the band gaps of a periodic Schrödinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1D and 2D localization below the ground state of such an operator. Furthermore, we extend our results to 1D and 2D localization in d dimensions; for example, by a linear or planar defect in a three-dimensional crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Attribution-Noncommercial-Share Alike 3.0 Unported
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevB.81.155324
