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Geometric Currents in Piezoelectricity

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185, Roma, Italy

    Gianluca Panati

  2. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK

    Christof Sparber

  3. Mathematics Institute, University Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Stefan Teufel

Authors
  1. Gianluca Panati
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  2. Christof Sparber
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  3. Stefan Teufel
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Correspondence to Gianluca Panati.

Additional information

Communicated by G. Friesecke

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Panati, G., Sparber, C. & Teufel, S. Geometric Currents in Piezoelectricity. Arch Rational Mech Anal 191, 387–422 (2009). https://doi.org/10.1007/s00205-008-0111-y

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  • DOI: https://doi.org/10.1007/s00205-008-0111-y

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