Geometric currents in piezoelectricity

Details Geometric currents in piezoelectricity Geometric currents in piezoelectricity

2006-06-19

arxiv.org/abs/math-ph/0606044v1

Arch. Rat. Mech. Analysis 191, 387-422 (2009)

Physics

Mathematical Physics

34 pages, no figures

Scientific paper

10.1007/s00205-008-0111-y

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.

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