Instanton calculus of Lifshitz tails
Name
PhysRevB.93.075120.pdf
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143.32 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Yaida, Sho
Date Issued
February 2016
Journal
Physical Review B
Publisher
American Physical Society
Citation
Yaida, Sho. “Instanton Calculus of Lifshitz Tails.” Physical Review B 93, no. 7 (February 9, 2016). © 2016 American Physical Society
Version
Final published version
Abstract
Some degree of quenched disorder is present in nearly all solids, and can have a marked impact on their macroscopic properties. A manifestation of this effect is the Lifshitz tail of localized states that then gets attached to the energy spectrum, resulting in the nonzero density of states in the band gap. We present here a systematic approach for deriving the asymptotic behavior of the density of states and of the typical shape of the disorder potentials in the Lifshitz tail. The analysis is carried out first for the well-controlled case of noninteracting particles moving in a Gaussian random potential and then for a broad class of disordered scale-invariant models—pertinent to a variety of systems ranging from semiconductors to semimetals to quantum critical systems. For relevant Gaussian disorder, we obtain the general expression for the density of states deep in the tail, with the rate of exponential suppression governed by the dynamical exponent and spatial dimensions. For marginally relevant disorder, however, we would expect a power-law scaling. We discuss the implications of these results for understanding conduction in disordered materials.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.93.075120
