Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
Mesoscale and Nanoscale Physics
2009-02-19 v3 High Energy Physics - Theory
Abstract
A generalized Peierls substitution which takes into account a Berry phase term must be considered for the semiclassical treatment of electrons in a magnetic field. This substitution turns out to be an essential element for the correct determination of the semiclassical equations of motion as well as for the semiclassical Bohr-Sommerfeld quantization condition for energy levels. A general expression for the cross-sectional area is derived and used as an illustration for the calculation of the energy levels of Bloch and Dirac electrons.
Keywords
Cite
@article{arxiv.0805.2455,
title = {Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution},
author = {Pierre Gosselin and Hocine Boumrar and Herve Mohrbach},
journal= {arXiv preprint arXiv:0805.2455},
year = {2009}
}