Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: an Hamiltonian Approach

Pierre Gosselin (1) , Fehrat Ménas (2) , Alain Bérard (3) , Hervé Mohrbach (3)

1 IF - Institut Fourier
2 LPCQ - Laboratoire de Physique et Chimie Quantique [Tizi-Ouzou]
3 FCN - Fédération de Chimie de Nancy

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. Contrary to previous treatment based on the study of electron wave-packets dynamics, it is found that both the position and momentum are Berry-phase dependent. This allows us to find a well defined semi-classical Hamiltonian in the presence of Berry-phase terms. The resulting equations of motion turn out to be only formally equivalent to previous ones derived from wave-packets dynamics. Besides, our method is more general as we are not limited to the uniform magnetic field case.

Mots clés: Magnetic Bloch Bands; Berry phase; semiclassical equations of motion; Liouville theorem

Domaines: Autre [cond-mat.other]

Pierre Gosselin, Fehrat Ménas, Alain Bérard, Hervé Mohrbach. Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: an Hamiltonian Approach. 2006. ⟨hal-00017432v1⟩