Europhys. Lett.
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
Europhys. Lett., 76 (4), pp. 651-656 (2006)
DOI: 10.1209/epl/i2006-10321-4

Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach

P. Gosselin1, F. Ménas2, A. Bérard3 and H. Mohrbach3

1  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

received 24 May 2006; accepted in final form 25 September 2006
published online 13 October 2006

By formally diagonalizing with accuracy $\hbar$ 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.

72.15.-v - Electronic conduction in metals and alloys.
72.10.-d - Theory of electronic transport; scattering mechanisms.

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