2023/12/22 by Jinhong Park, Park, Jin-Hong, Jun‐Won Rhim +1 · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mechanical and Optical Resonators #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2312.14553
openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 compact localized state(NCLS). The partially flat band develops only in a momentum range, where normalizable Bloch wave functions can be obtained by the linear combination of the NCLSs. Outside this momentum region, a ghost flat band, unseen from the band structure, is introduced for the consistent counting argument with the full set of NCLSs. Then, we demonstrate that the Wannier function corresponding to the partially flat band exhibits an algebraic(∼ 1/r1+ε in 1D and ∼ 1/r3/2+ε in 2D) decay behavior, where ε is a positive number. Namely, one can have the Wannier obstruction even in a topologically trivial band if it is partially flat. Finally, we develop a construction scheme of a tight-binding model of the topological semimetal by designing an NCLS.