Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

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Abstract

We study a one-dimensional quasiperiodic system described by the Aubry–André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry–André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value Vc, and thus no mobility edge exists. However, it was shown in a recent work that for the system with V < Vc and the wave vector α of the incommensurate potential is small, there exist almost mobility edges at the energy Ec±, which separate the robustly delocalized states from “almost localized” states. We find that, besides Ec±, there exist additionally another energy edges Ec′±, at which abrupt change of inverse participation ratio (IPR) occurs. By using the IPR and carrying out multifractal analyses, we identify the existence of critical regions among |Ec±| ≤ |E| ≤ |Ec′±| with the mobility edges Ec± and Ec′± separating the critical region from the extended and localized regions, respectively. We also study the system with V > Vc, for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry–André model.

Keywords

Solid State and Materials 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of SciencesBeijingP.R. China
  2. 2.School of Physical Sciences, University of Chinese Academy of SciencesBeijingP.R. China
  3. 3.Department of PhysicsZhejiang Normal UniversityJinhuaP.R. China
  4. 4.Collaborative Innovation Center of Quantum MatterBeijingP.R. China

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