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Topology in the Sierpiński-Hofstadter problem


Brzezińska, Marta; Cook, Ashley M; Neupert, Titus (2018). Topology in the Sierpiński-Hofstadter problem. Physical review. B, 98(20):205116.

Abstract

Using the Sierpiński carpet and gasket, we investigate whether fractal lattices embedded in two-dimensional space can support topological phases when subjected to a homogeneous external magnetic field. To this end, we study the localization property of eigenstates, the Chern number, and the evolution of energy level statistics when disorder is introduced. Combining these theoretical tools, we identify regions in the phase diagram of both the carpet and the gasket, for which the systems exhibit properties normally associated with gapless topological phases with a mobility edge.

Abstract

Using the Sierpiński carpet and gasket, we investigate whether fractal lattices embedded in two-dimensional space can support topological phases when subjected to a homogeneous external magnetic field. To this end, we study the localization property of eigenstates, the Chern number, and the evolution of energy level statistics when disorder is introduced. Combining these theoretical tools, we identify regions in the phase diagram of both the carpet and the gasket, for which the systems exhibit properties normally associated with gapless topological phases with a mobility edge.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Electronic, Optical and Magnetic Materials
Physical Sciences > Condensed Matter Physics
Language:English
Date:8 November 2018
Deposited On:25 Jan 2019 13:43
Last Modified:29 Jul 2020 09:10
Publisher:American Physical Society
ISSN:2469-9950
OA Status:Green
Publisher DOI:https://doi.org/10.1103/physrevb.98.205116
Project Information:
  • : FunderSNSF
  • : Grant ID200021_169061
  • : Project TitleAnyons in topological matter: From axiomatic field theory to advanced materials

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