dc conductivity as a geometric phase
Author
Hetényi, B.
Date
2013Source 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
ArticleItem Usage Stats
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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.