The Electronic Structure of Smoothly Deformed Crystals: Wannier Functions and the Cauchy-Born Rule

Weinan E, Jianfeng Lu

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

The electronic structure of a smoothly deformed crystal is analyzed for the case when the effective Hamiltonian is a given function of the nuclei by considering the regime when the scale of the deformation is much larger than the lattice parameter. Wannier functions are defined by projecting the Wannier functions for the undeformed crystal to the space spanned by the wave functions of the deformed crystal. The exponential decay of such Wannier functions is proved for the case when the undeformed crystal is an insulator. The celebrated Cauchy-Born rule for crystal lattices is extended to the present situation for electronic structure analysis.

Original languageEnglish (US)
Pages (from-to)407-433
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Volume199
Issue number2
DOIs
StatePublished - Jan 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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