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Quasi-localization and Wannier obstruction in partially flat bands.
- Source :
-
Communications Physics . 6/4/2024, Vol. 7 Issue 1, p1-7. 7p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BLOCH waves
*WAVE functions
*BAND gaps
Subjects
Details
- Language :
- English
- ISSN :
- 23993650
- Volume :
- 7
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Communications Physics
- Publication Type :
- Academic Journal
- Accession number :
- 177674659
- Full Text :
- https://doi.org/10.1038/s42005-024-01679-6