{"title":"Quasi-localization and Wannier obstruction in partially flat bands","authors":"Jin-Hong Park, Jun-Won Rhim","doi":"10.1038/s42005-024-01679-6","DOIUrl":null,"url":null,"abstract":"The localized nature of a flat band is understood by the existence of a compact localized eigenstate. However, the localization properties of a partially flat band, ubiquitous in surface modes of topological semimetals, have been unknown. We show that the partially flat band is characterized by a non-normalizable quasi-compact localized state (Q-CLS), which is compactly localized along several directions but extended in at least one direction. The partially flat band develops at momenta where normalizable Bloch wave functions can be obtained from a linear combination of the non-normalizable Q-CLSs. Outside this momentum region, a ghost flat band, unseen from the band structure, is introduced based on a counting argument. Then, we demonstrate that the Wannier function corresponding to the partially flat band exhibits an algebraic decay behavior. Namely, one can have the Wannier obstruction in a band with a vanishing Chern number if it is partially flat. Finally, we develop the construction scheme of a tight-binding model for a topological semimetal by designing a Q-CLS. Compact localized states constitute an auxiliary state representation for a flat-band lattice system with wave functions non-zero only in a finite portion of the lattice. Here, the authors show that in some flat-band systems, these states can be partially “hidden”; surprisingly, these ghost flat bands present an obstruction to be represented as maximally localized Wannier functions.","PeriodicalId":10540,"journal":{"name":"Communications Physics","volume":null,"pages":null},"PeriodicalIF":5.4000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s42005-024-01679-6.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Physics","FirstCategoryId":"101","ListUrlMain":"https://www.nature.com/articles/s42005-024-01679-6","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The localized nature of a flat band is understood by the existence of a compact localized eigenstate. However, the localization properties of a partially flat band, ubiquitous in surface modes of topological semimetals, have been unknown. We show that the partially flat band is characterized by a non-normalizable quasi-compact localized state (Q-CLS), which is compactly localized along several directions but extended in at least one direction. The partially flat band develops at momenta where normalizable Bloch wave functions can be obtained from a linear combination of the non-normalizable Q-CLSs. Outside this momentum region, a ghost flat band, unseen from the band structure, is introduced based on a counting argument. Then, we demonstrate that the Wannier function corresponding to the partially flat band exhibits an algebraic decay behavior. Namely, one can have the Wannier obstruction in a band with a vanishing Chern number if it is partially flat. Finally, we develop the construction scheme of a tight-binding model for a topological semimetal by designing a Q-CLS. Compact localized states constitute an auxiliary state representation for a flat-band lattice system with wave functions non-zero only in a finite portion of the lattice. Here, the authors show that in some flat-band systems, these states can be partially “hidden”; surprisingly, these ghost flat bands present an obstruction to be represented as maximally localized Wannier functions.
期刊介绍:
Communications Physics is an open access journal from Nature Research publishing high-quality research, reviews and commentary in all areas of the physical sciences. Research papers published by the journal represent significant advances bringing new insight to a specialized area of research in physics. We also aim to provide a community forum for issues of importance to all physicists, regardless of sub-discipline.
The scope of the journal covers all areas of experimental, applied, fundamental, and interdisciplinary physical sciences. Primary research published in Communications Physics includes novel experimental results, new techniques or computational methods that may influence the work of others in the sub-discipline. We also consider submissions from adjacent research fields where the central advance of the study is of interest to physicists, for example material sciences, physical chemistry and technologies.