Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
arXiv:0805.2455 · doi:10.1209/0295-5075/84/50002
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.
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