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Flat bands with band crossings enforced by symmetry representation

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Title
Flat bands with band crossings enforced by symmetry representation
Author(s)
Yoonseok Hwang; Jun-Won Rhim; Bohm-Jung Yang
Subject
HUBBARD-MODEL, ; FERROMAGNETISM
Publication Date
2021-08-05
Journal
PHYSICAL REVIEW B, v.104, no.8
Publisher
American Physical Society
Abstract
© 2021 American Physical Society.Flat bands have band crossing points with other dispersive bands in many systems including the canonical flat-band models in the Lieb and kagome lattices. Here we show that some of such band degeneracy points of nondegenerate flat bands are unavoidable because of the symmetry representation (SR) of flat bands under unitary symmetry. We refer to such a band degeneracy point of flat bands as a SR-enforced band crossing. SR-enforced band crossing is distinct from the conventional band degeneracy protected by symmetry eigenvalues or topological charges in that its protection requires both specific symmetry representation and band flatness of the flat band, simultaneously. Even n-fold rotation Cn (n=2,3,4,6) symmetry, which cannot protect band degeneracy without additional symmetries due to its abelian nature, can protect SR-enforced band crossings in flat-band systems. In two-dimensional flat-band systems with Cn symmetry, when the degeneracy of a SR-enforced band crossing is lifted by a Cn symmetry-preserving perturbation, we obtain a nearly flat Chern band. Our theory not only explains the origin of the band crossing points of FBs existing in various models, but also gives a strict no-go theorem for isolated FBs in a given lattice arising from the SR.
URI
https://pr.ibs.re.kr/handle/8788114/10172
DOI
10.1103/PhysRevB.104.L081104
ISSN
2469-9950
Appears in Collections:
Center for Correlated Electron Systems(강상관계 물질 연구단) > 1. Journal Papers (저널논문)
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