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Localization, phases and transitions in the three-dimensional extended Lieb lattices
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Liu, Jie, Mao, Xiaoyu, Zhong, Jianxin and Römer, Rudolf A. (2020) Localization, phases and transitions in the three-dimensional extended Lieb lattices. Physical Review B (Condensed Matter and Materials Physics), 102 (17). 174207 . doi:10.1103/PhysRevB.102.174207 ISSN 1098-0121.
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Official URL: https://doi.org/10.1103/PhysRevB.102.174207
Abstract
We study the localization properties and the Anderson transition in the 3D Lieb lattice L3(1) and its extensions L3(n) in the presence of disorder. We compute the positions of the flat bands, the disorder-broadened density of states and the energy-disorder phase diagrams for up n = 4. Via finite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent ν. We find that the critical disorder Wc decreases from ∼ 16.5 for the cubic lattice, to ∼ 8.6 for L3(1), ∼ 5.9 for L3(2) and ∼ 4.8 for L3(3). Nevertheless, the value of the critical exponent ν for all Lieb lattices studied here and across various disorder and energy transitions agrees within error bars with the generally accepted universal value ν = 1.590 (1.579, 1.602).
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Lattice theory, Energy bands | |||||||||||||||
Journal or Publication Title: | Physical Review B (Condensed Matter and Materials Physics) | |||||||||||||||
Publisher: | American Physical Society | |||||||||||||||
ISSN: | 1098-0121 | |||||||||||||||
Official Date: | 1 November 2020 | |||||||||||||||
Dates: |
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Volume: | 102 | |||||||||||||||
Number: | 17 | |||||||||||||||
Article Number: | 174207 | |||||||||||||||
DOI: | 10.1103/PhysRevB.102.174207 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Reuse Statement (publisher, data, author rights): | © 2020 American Physical Society | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Copyright Holders: | ©2020 American Physical Society | |||||||||||||||
Date of first compliant deposit: | 28 October 2020 | |||||||||||||||
Date of first compliant Open Access: | 29 October 2020 | |||||||||||||||
RIOXX Funder/Project Grant: |
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