ar X iv : 1 21 2 . 40 47 v 4 [ co nd - m at . o th er ] 1 8 Ju n 20 13 dc conductivity as a geometric phase

نویسنده

  • Balázs Hetényi
چکیده

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 [Phys. Rev. 133 A171 (1964)], namely, that insulation is due to localization in the many-body space, is refined as follows. Wavefunctions which are eigenfunctions of the total current operator give rise to a finite Dc and are therefore metallic. These states 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 eΦB Nhc = Q M , with Q and M integers.

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تاریخ انتشار 2013