Volume 120, Number 3, November 2017
|Number of page(s)||7|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||22 January 2018|
Wave function correlations and the AC conductivity of disordered wires beyond the Mott-Berezinskii law
1 Amsterdam University of Applied Studies - Weesperzijde 190, 1097 DZ, Amsterdam, the Netherlands
2 Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique - F-69342 Lyon, France
3 Ohio State University, Department of Physics - 191 W. Woodruff Ave, Columbus, OH, 43210, USA
Received: 24 August 2017
Accepted: 3 January 2018
In one-dimensional disordered wires electronic states are localized at any energy. Correlations of the states at close positive energies and the AC conductivity in the limit of small frequency are described by the Mott-Berezinskii theory. We revisit the instanton approach to the statistics of wave functions and AC transport valid in the tails of the spectrum (large negative energies). Applying our recent results on functional determinants, we calculate exactly the integral over Gaussian fluctuations around the exact two-instanton saddle point. We derive correlators of wave functions at different energies beyond the leading order in the energy difference. This allows us to calculate corrections to the Mott-Berezinskii law (the leading small-frequency asymptotic behavior of ) which approximate the exact result in a broad range of ω. We compare our results with the ones obtained for positive energies.
PACS: 72.15.Rn – Localization effects (Anderson or weak localization) / 73.21.Hb – Quantum wires / 73.22.Dj – Single particle states
© EPLA, 2018
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