Bulk-interface correspondence from quantum distance in flat band systems

Chang geun Oh; Doohee Cho; Se Young Park; Jun Won Rhim

doi:10.1038/s42005-022-01102-y

Bulk-interface correspondence from quantum distance in flat band systems

Chang geun Oh, Doohee Cho, Se Young Park, Jun Won Rhim

Department of Physics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes.

Original language	English
Article number	320
Journal	Communications Physics
Volume	5
Issue number	1
DOIs	https://doi.org/10.1038/s42005-022-01102-y
Publication status	Published - 2022 Dec

Bibliographical note

Funding Information:
C.-g.O. and J.-W.R. were supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (Grant No. 2021R1A2C1010572). J.-W.R. was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (Grant No. 2021R1A5A1032996) and Creation of the Quantum Information Science R&D Ecosystem (Grant No. 2022M3H3A106307411) through the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science and ICT). D.C. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant No. 2020R1C1C1007895 and 2017R1A5A1014862) and the Yonsei University Research Fund of 2019-22-0209. S.Y.P. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant No. 2021R1C1C1009494) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2021R1A6A1A03043957).

Publisher Copyright:
© 2022, The Author(s).

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1038/s42005-022-01102-y

Cite this

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title = "Bulk-interface correspondence from quantum distance in flat band systems",

abstract = "The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes.",

author = "Oh, {Chang geun} and Doohee Cho and Park, {Se Young} and Rhim, {Jun Won}",

note = "Funding Information: C.-g.O. and J.-W.R. were supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (Grant No. 2021R1A2C1010572). J.-W.R. was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (Grant No. 2021R1A5A1032996) and Creation of the Quantum Information Science R&D Ecosystem (Grant No. 2022M3H3A106307411) through the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science and ICT). D.C. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant No. 2020R1C1C1007895 and 2017R1A5A1014862) and the Yonsei University Research Fund of 2019-22-0209. S.Y.P. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant No. 2021R1C1C1009494) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2021R1A6A1A03043957). Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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N2 - The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes.

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Bulk-interface correspondence from quantum distance in flat band systems

Abstract

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