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• W2714678368 abstract "We introduce and explore a family of self-dual models of single-particle motion in quasiperiodic potentials, with hopping amplitudes that fall off as a power law with exponent $p$. These models are generalizations of the familiar Aubry-Andre model. For large enough $p$, their static properties are similar to those of the Aubry-Andre model, although the low-frequency conductivity in the localized phase is sensitive to $p$. For $p leq 2.1$ the Aubry-Andre localization transition splits into three transitions; two distinct intermediate regimes with both localized and delocalized states appear near the self-dual point of the Aubry-Andre model. In the intermediate regimes, the density of states is singular continuous in much of the spectrum, and is approximately self-similar: states form narrow energy bands, which are divided into yet narrower sub-bands; we find no clear sign of a mobility edge. When $p < 1$, localized states are not stable in random potentials; in the present model, however, tightly localized states are present for relatively large systems. We discuss the frequency-dependence and strong sample-to-sample fluctuations of the low-frequency optical conductivity, although a suitably generalized version of Mott's law is recovered when the power-law is slowly decaying. We present evidence that many of these features persist in models that are away from self-duality." @default.
• W2714678368 created "2017-06-30" @default.
• W2714678368 creator A5056107519 @default.
• W2714678368 date "2017-08-07" @default.
• W2714678368 modified "2023-10-17" @default.
• W2714678368 title "Self-dual quasiperiodic systems with power-law hopping" @default.
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• W2714678368 doi "https://doi.org/10.1103/physrevb.96.054202" @default.
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