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Singular flat bands

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Title
Singular flat bands
Author(s)
Jun-Won Rhim; Bohm-Jung Yang
Publication Date
2021-04
Journal
Advances in Physics: X, v.6, no.1
Publisher
Taylor and Francis Ltd.
Abstract
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band’s Bloch wave functions. We first explain that the flat bands can be classified into two classes: singular and non-singular flat bands, based on the presence or absence of the singularity in the flat band’s Bloch wave functions. The singularity is generated by the band crossing of the flat band with another dispersive band. In the singular flat band, one can find a special kind of eigenmodes, called the non-contractible loop states and the robust boundary modes, which exhibit nontrivial real-space topology. Then, we review the experimental realization of these topological eigenmodes of the flat band in the photonic lattices. While the singularity of the flat band is topologically trivial, we show that the maximum quantum distance around the singularity is a bulk invariant representing the strength of the singularity which protects the robust boundary modes. Finally, we discuss how the maximum quantum distance or the strength of the singularity manifests itself in the anomalous Landau level spreading of the singular flat band when it has a quadratic band-crossing with another band.
URI
https://pr.ibs.re.kr/handle/8788114/9725
DOI
10.1080/23746149.2021.1901606
ISSN
2374-6149
Appears in Collections:
Center for Correlated Electron Systems(강상관계 물질 연구단) > 1. Journal Papers (저널논문)
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