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

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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• Electric Field Effect in Atomically Thin Carbon Films
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• Topological spin transport of relativistic electron
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Cited by in corpus (1)

• Bloch electrons interacting with an external electromagnetic field and Bloch electrons in interaction