Semiclassical quantization of electrons in magnetic fields: The generalized Peierls substitutionP. Gosselin1, H. Boumrar2, 3 and H. Mohrbach2
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
received 22 September 2008; accepted in final form 21 October 2008; published December 2008
published online 26 November 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.
03.65.Sq - Semiclassical theories and applications.
03.65.Vf - Phases: geometric; dynamic or topological.
© EPLA 2008