Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution

Details Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution

2008-05-16

arxiv.org/abs/0805.2455v3

Europhysics Letters (EPL) 84 (2008) 50002

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1209/0295-5075/84/50002

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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