Geometric currents in piezoelectricity

Abstract

As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adiabatic limit the macroscopic current is determined by the geometry of the Bloch bundle. As a consequence we obtain the King-Smith and Vanderbilt formula up to errors smaller than any power of the adiabatic parameter.

34 pages, no figures

References in corpus (6)

• Maximally-localized generalized Wannier functions for composite energy bands
• Berry phase correction to electron density of states in solids
• The Non-Commutative Geometry of the Quantum Hall Effect
• Triviality of Bloch and Bloch-Dirac bundles
• Effective dynamics for Bloch electrons: Peierls substitution and beyond
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Cited by in corpus (11)

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• Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields
• Topological Polarization in Graphene-like Systems
• Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators
• Topological invariants of eigenvalue intersections and decrease of Wannier functions in graphene
• Semiclassical approximations for adiabatic slow-fast systems
• Approximate controllability of the Jaynes-Cummings dynamics