1. Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
- Author
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Pierre Gosselin, Hocine Boumrar, Hervé Mohrbach, Gosselin-Lotz, Pierre, Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Instituut-Lorentz, Universiteit Leiden [Leiden], Laboratoire de physique moléculaire et des collisions (LPMC), Université Paul Verlaine - Metz (UPVM), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Laboratoire de Physique et Chimie Quantique [Tizi-Ouzou] (LPCQ ), Université Mouloud Mammeri [Tizi Ouzou] (UMMTO), Fédération de Chimie de Nancy (FCN), and Université Henri Poincaré - Nancy 1 (UHP)-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
High Energy Physics - Theory ,[PHYS.COND.CM-SCE] Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] ,FOS: Physical sciences ,General Physics and Astronomy ,Semiclassical physics ,Electron ,01 natural sciences ,010305 fluids & plasmas ,Quantization (physics) ,Dirac electron ,[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,010306 general physics ,General expression ,[PHYS.COND.CM-MSQHE]Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall] ,ComputingMilieux_MISCELLANEOUS ,[PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph] ,Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Equations of motion ,Magnetic field ,Nonlinear Sciences::Chaotic Dynamics ,High Energy Physics - Theory (hep-th) ,Geometric phase ,[PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] - Abstract
International audience; 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.
- Published
- 2008