Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a 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

y 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.

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: a Hamiltonian Approach. EPL - Europhysics Letters, 2006, 76 (4), pp.651-656. ⟨10.1209/epl/i2006-10321-4⟩. ⟨hal-00017432v2⟩