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

Pierre Gosselin (1) , Hocine Boumrar (2) , Herve Mohrbach (3, 4)

1 IF - Institut Fourier
2 LPCQ - Laboratoire de Physique et Chimie Quantique [Tizi-Ouzou]
3 FCN - Fédération de Chimie de Nancy
4 LPMC - Laboratoire de physique moléculaire et des collisions

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.

Domains: Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall]; High Energy Physics - Theory [hep-th]

Pierre Gosselin, Hocine Boumrar, Herve Mohrbach. Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution. 2008. ⟨hal-00279987v2⟩