Orthogonal localized wave functions of an electron in a magnetic field

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)...

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Bibliographic Details
Main Authors Rashba, E. I, Zhukov, L. E, Efros, A. L
Format Journal Article
LanguageEnglish
Published 05.03.1996
Subjects
Physics - Disordered Systems and Neural Networks
Physics - Materials Science
Physics - Mesoscale and Nanoscale Physics
Physics - Other Condensed Matter
Physics - Quantum Gases
Physics - Soft Condensed Matter
Physics - Statistical Mechanics
Physics - Strongly Correlated Electrons
Physics - Superconductivity
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Summary: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.
DOI:10.48550/arxiv.cond-mat/9603037