| Issue |
Europhys. Lett.
Volume 76, Number 4, November 2006
|
|
|---|---|---|
| Page(s) | 651 - 656 | |
| Section | Condensed matter: electronic structure, electrical, magnetic, and optical properties | |
| DOI | https://doi.org/10.1209/epl/i2006-10321-4 | |
| Published online | 13 October 2006 | |
Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach
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:
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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