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강상관계 물질 연구단
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Classification of flat bands according to the band-crossing singularity of Bloch wave functions

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Title
Classification of flat bands according to the band-crossing singularity of Bloch wave functions
Author(s)
Jun-Won Rhim; Bohm-Jung Yang
Publication Date
2019-01
Journal
PHYSICAL REVIEW B, v.99, no.4, pp.045107 -
Publisher
AMER PHYSICAL SOC
Abstract
We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the flat band cannot be defined. This singularity precludes the compact localized states from forming a complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a nonsingular flat band has no singularity, and thus forms a vector bundle. A nonsingular flat band can be completely isolated from other bands while preserving the perfect flatness. All one-dimensional flat bands belong to the nonsingular class. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the flat band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in flat bands. © 2019 American Physical Society
URI
https://pr.ibs.re.kr/handle/8788114/5598
ISSN
2469-9950
Appears in Collections:
Center for Correlated Electron Systems(강상관계 물질 연구단) > Journal Papers (저널논문)
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