| Issue |
EPL
Volume 84, Number 5, December 2008
|
|
|---|---|---|
| Article Number | 50002 | |
| Number of page(s) | 5 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/84/50002 | |
| Published online | 26 November 2008 | |
Semiclassical quantization of electrons in magnetic fields: The generalized Peierls substitution
1
Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques, Université Grenoble I BP 74, 38402 Saint Martin d'Hères, Cedex, France, EU
2
Laboratoire de Physique Moléculaire et des Collisions, ICPMB-FR CNRS 2843, Université Paul Verlaine-Metz 57078 Metz Cedex 3, France, EU
3
Laboratoire de Physique et Chimie Quantique, Université Mouloud Mammeri - BP 17, Tizi Ouzou, Algerie
Corresponding author: mohrbach@univ-metz.fr
Received:
22
September
2008
Accepted:
21
October
2008
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 energy levels of Bloch and Dirac electrons.
PACS: 03.65.Sq – Semiclassical theories and applications / 03.65.Vf – Phases: geometric; dynamic or topological
© EPLA, 2008
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