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      dc conductivity as a geometric phase

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      Author
      Hetényi, B.
      Date
      2013
      Source Title
      Physical Review B - Condensed Matter and Materials Physics
      Print ISSN
      1098-0121
      Publisher
      American Physical Society
      Volume
      87
      Issue
      23
      Pages
      235123-1 - 235123-6
      Language
      English
      Type
      Article
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      Abstract
      The zero-frequency conductivity (Dc), the criterion to distinguish between conductors and insulators, is expressed in terms of a geometric phase. Dc is also expressed using the formalism of the modern theory of polarization. The tenet of Kohn, namely that insulation is due to localization in the many-body space, is refined as follows. Wave functions, which are eigenfunctions of the total current operator, give rise to a finite Dc and are therefore metallic. They are also delocalized. Based on the value of Dc it is also possible to distinguish purely metallic states from states in which the metallic and insulating phases coexist. Several examples which corroborate the results are presented, as well as a numerical implementation. The formalism is also applied to the Hall conductance, and the quantization condition for zero Hall conductance is derived to be eΦBNhc=QM, with Q and M as integers.
      Permalink
      http://hdl.handle.net/11693/20928
      Published Version (Please cite this version)
      http://dx.doi.org/10.1103/PhysRevB.87.235123
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