1. Quasi-localization and Wannier obstruction in partially flat bands.
- Author
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Park, Jin-Hong and Rhim, Jun-Won
- Subjects
- *
BLOCH waves , *WAVE functions , *BAND gaps - 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]
- Published
- 2024
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