Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps
Other Condensed Matter
2010-04-29 v3
Abstract
We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrodinger 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, a linear or planar defect in a 3d crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.
Keywords
Cite
@article{arxiv.1002.4426,
title = {Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps},
author = {Arthur Parzygnat and Karen K. Y. Lee and Yehuda Avniel and Steven G. Johnson},
journal= {arXiv preprint arXiv:1002.4426},
year = {2010}
}
Comments
9 pages, 3 figures