Orthogonal localized wave functions of an electron in a magnetic field
Abstract
We prove the existence of a set of twoscale magnetic Wannier orbitals, w_{mn}(r), in 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}(r) localized at the origin has a nearly Gaussian shape of exp(r^{2}/4l^{2})/2π for r<~2πl, 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 complete basis for manyelectron problems.
 Publication:

Physical Review B
 Pub Date:
 February 1997
 DOI:
 10.1103/PhysRevB.55.5306
 arXiv:
 arXiv:condmat/9603037
 Bibcode:
 1997PhRvB..55.5306R
 Keywords:

 Condensed Matter
 EPrint:
 RevTex, 18 pages, 5 ps fig