Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach
arXiv:cond-mat/0601472 · doi:10.1209/epl/i2006-10321-4
Abstract
y 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.
4 pages
References in corpus (4)
- Dissipationless Quantum Spin Current at Room Temperature
- Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
- Topological spin transport of relativistic electron
- On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
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