Volume 76, Number 4, November 2006
|Page(s)||651 - 656|
|Section||Condensed matter: electronic structure, electrical, magnetic, and optical properties|
|Published online||13 October 2006|
Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach
Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathématiques Université Grenoble I - BP 74, 38402 Saint Martin d'Hères, Cedex, France
2 Laboratoire de Physique et de Chimie Quantique, Faculté des Sciences Université Mouloud Mammeri - BP 17, Tizi Ouzou, Algerie
3 Laboratoire de Physique Moléculaire et des Collisions, ICPMB-FR CNRS 2843 Université Paul Verlaine-Metz - 1 boulevard Arago, 57078 Metz Cedex 3, France
Accepted: 25 September 2006
By formally diagonalizing with accuracy the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase corrections, and therefore confirm the validity of the Liouville theorem. We show that both the position and momentum operators acquire a Berry-phase dependence, leading to a non-canonical Hamiltonian dynamics. The equations of motion turn out to be identical to the ones previously derived in the context of electron wave-packets dynamics.
PACS: 72.15.-v – Electronic conduction in metals and alloys / 72.10.-d – Theory of electronic transport; scattering mechanisms
© EDP Sciences, 2006
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