{"title":"Resonances, mobility edges, and gap-protected Anderson localization in generalized disordered mosaic lattices","authors":"Stefano Longhi","doi":"10.1103/physrevb.110.184201","DOIUrl":null,"url":null,"abstract":"Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges, and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally spaced site within the lattice, with a spacing <mjx-container ctxtmenu_counter=\"56\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(3 0 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"inequality\" data-semantic-speech=\"upper M greater than or equals 2\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,≥\" data-semantic-parent=\"3\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>≥</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container>. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang <i>et al.</i>, <span>Phys. Rev. Lett.</span> <b>125</b>, 196604 (2020).]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.184201","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges, and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally spaced site within the lattice, with a spacing 𝑀≥2. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang et al., Phys. Rev. Lett.125, 196604 (2020).]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice.
镶嵌晶格模型是最近提出的一类特殊的无序系统,具有共振能量、多迁移率边缘和反常输运特性。在这类系统中,现场势能无序(不相关或不相称)仅在晶格内每个等间距位点引入,间距𝑀≥2。无序镶嵌晶格的一个显著特性是在某些共振频率上存在扩展态,即使在强无序状态下也能阻止安德森的完全定位。在此,我们引入了一类更广泛的镶嵌晶格,并推导出了不相称正弦无序的流动边缘和局域化长度的一般表达式,这是对先前结果的推广[Y. Wang 等人,Phys.对于不相称无序和不相关无序,我们都证明了安德森定位受到无序晶格开放间隙的保护,并推导出完全安德森定位的一些一般标准。通过考虑一些模型,如镶嵌苏-施里弗-希格(SSH)模型和三聚镶嵌晶格,对结果进行了说明。
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
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