Orthogonal localized wave functions of an electron in a magnetic field
Condensed Matter
2009-10-28 v3
Abstract
We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.
Keywords
Cite
@article{arxiv.cond-mat/9603037,
title = {Orthogonal localized wave functions of an electron in a magnetic field},
author = {E. I. Rashba and L. E. Zhukov and A. L. Efros},
journal= {arXiv preprint arXiv:cond-mat/9603037},
year = {2009}
}
Comments
RevTex, 18 pages, 5 ps fig