
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
Chang-Hwan Yi (yichanghwan@hanmail.net)
Hee Chul Park (hcpark@ibs.re.kr)
Moon Jip Park (moonjippark@ibs.re.kr)
Published:31 October 2022,
Published Online:06 October 2022,
Received:17 February 2022,
Revised:14 August 2022,
Accepted:31 August 2022
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Yi, C. H., Park, H. C. & Park, M. J. Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices. Light: Science & Applications, 11, 2523-2529 (2022).
Yi, C. H., Park, H. C. & Park, M. J. Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices. Light: Science & Applications, 11, 2523-2529 (2022). DOI: 10.1038/s41377-022-00977-4.
The moiré superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work
we propose a photonic analog of the moiré superlattice based on dielectric resonator quasi-atoms. In sharp contrast to van der Waals materials with weak interlayer coupling
we realize the strong coupling regime in a moiré superlattice
characterized by cascades of robust flat bands at large twist-angles. Surprisingly
we find that these flat bands are characterized by a non-trivial band topology
the origin of which is the moiré pattern of the resonator arrangement. The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on edge
protected by the reflection symmetry of the moiré superlattice. By explicitly breaking the underlying reflection symmetry on the boundary terminations
we show that the first-order topological edge modes naturally deform into higher-order topological corner modes. Our work pioneers the physics of topological phases in the designable platform of photonic moiré superlattices beyond the weakly coupled regime.
E. Y. Andrei , A. H. MacDonald . Graphene bilayers with a twist . Nat. Mater. , 2020 . 19 1265 -1275 . DOI:10.1038/s41563-020-00840-0http://doi.org/10.1038/s41563-020-00840-0 .
Y. Cao , 等 . Unconventional superconductivity in magic-angle graphene superlattices . Nature , 2018 . 556 43 -50 . DOI:10.1038/nature26160http://doi.org/10.1038/nature26160 .
Y. Cao , 等 . Correlated insulator behaviour at half-filling in magic-angle graphene superlattices . Nature , 2018 . 556 80 -84 . DOI:10.1038/nature26154http://doi.org/10.1038/nature26154 .
X. B. Lu , 等 . Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene . Nature , 2019 . 574 653 -657 . DOI:10.1038/s41586-019-1695-0http://doi.org/10.1038/s41586-019-1695-0 .
A. Kerelsky , 等 . Maximized electron interactions at the magic angle in twisted bilayer graphene . Nature , 2019 . 572 95 -100 . DOI:10.1038/s41586-019-1431-9http://doi.org/10.1038/s41586-019-1431-9 .
Z. D. Song , 等 . All magic angles in twisted bilayer graphene are topological . Phys. Rev. Lett. , 2019 . 123 036401 DOI:10.1103/PhysRevLett.123.036401http://doi.org/10.1103/PhysRevLett.123.036401 .
M. J. Park , 等 . Higher-order topological insulator in twisted bilayer graphene . Phys. Rev. Lett. , 2019 . 123 216803 DOI:10.1103/PhysRevLett.123.216803http://doi.org/10.1103/PhysRevLett.123.216803 .
B. Liu , 等 . Higher-order band topology in twisted Moiré superlattice . Phys. Rev. Lett. , 2021 . 126 066401 DOI:10.1103/PhysRevLett.126.066401http://doi.org/10.1103/PhysRevLett.126.066401 .
R. Bistritzer , A. H. MacDonald . Moiré bands in twisted double-layer graphene . Proc. Natl Acad. Sci. USA , 2011 . 108 12233 -12237 . DOI:10.1073/pnas.1108174108http://doi.org/10.1073/pnas.1108174108 .
T. Ozawa , 等 . Topological photonics . Rev. Mod. Phys. , 2019 . 91 015006 DOI:10.1103/RevModPhys.91.015006http://doi.org/10.1103/RevModPhys.91.015006 .
J. L. Chen , 等 . A perspective of twisted photonic structures . Appl. Phys. Lett. , 2021 . 119 240501 DOI:10.1063/5.0070163http://doi.org/10.1063/5.0070163 .
B. C. Lou , 等 . Theory for twisted bilayer photonic crystal slabs . Phys. Rev. Lett. , 2021 . 126 136101 DOI:10.1103/PhysRevLett.126.136101http://doi.org/10.1103/PhysRevLett.126.136101 .
K. C. Dong , 等 . Flat bands in magic-angle bilayer photonic crystals at small twists . Phys. Rev. Lett. , 2021 . 126 223601 DOI:10.1103/PhysRevLett.126.223601http://doi.org/10.1103/PhysRevLett.126.223601 .
M. Oudich , 等 . Photonic analog of bilayer graphene . Phys. Rev. B , 2021 . 103 214311 DOI:10.1103/PhysRevB.103.214311http://doi.org/10.1103/PhysRevB.103.214311 .
Y. C. Deng , 等 . Magic-angle bilayer phononic graphene . Phys. Rev. B , 2020 . 102 180304 DOI:10.1103/PhysRevB.102.180304http://doi.org/10.1103/PhysRevB.102.180304 .
P. Wang , 等 . Localization and delocalization of light in photonic moiré lattices . Nature , 2020 . 577 42 -46 . DOI:10.1038/s41586-019-1851-6http://doi.org/10.1038/s41586-019-1851-6 .
Q. D. Fu , 等 . Optical soliton formation controlled by angle twisting in photonic Moiré lattices . Nat. Photonics , 2020 . 14 663 -668 . DOI:10.1038/s41566-020-0679-9http://doi.org/10.1038/s41566-020-0679-9 .
H. Deng , 等 . Physics and applications of high-β micro- and nanolasers . Adv. Optical Mater. , 2021 . 9 2100415 DOI:10.1002/adom.202100415http://doi.org/10.1002/adom.202100415 .
M. Parto , 等 . Non-hermitian and topological photonics: optics at an exceptional point . Nanophotonics , 2021 . 10 403 -423 . DOI:10.1515/nanoph-2020-0434http://doi.org/10.1515/nanoph-2020-0434 .
J. M. B. Lopes dos Santos , N. M. R. Peres , A. H. Castro Neto . Graphene bilayer with a twist: Electronic structure . Phys. Rev. Lett. , 2007 . 99 256802 DOI:10.1103/PhysRevLett.99.256802http://doi.org/10.1103/PhysRevLett.99.256802 .
L. J. Zou , 等 . Band structure of twisted bilayer graphene: emergent symmetries, commensurate approximants, and Wannier obstructions . Phys. Rev. B , 2018 . 98 085435 DOI:10.1103/PhysRevB.98.085435http://doi.org/10.1103/PhysRevB.98.085435 .
J. Wiersig . Boundary element method for resonances in dielectric microcavities . J. Opt. A: Pure Appl. Opt. , 2003 . 5 53 -60 . DOI:10.1088/1464-4258/5/1/308http://doi.org/10.1088/1464-4258/5/1/308 .
P. A. Knipp , T. L. Reinecke . Boundary-element method for the calculation of electronic states in semiconductor nanostructures . Phys. Rev. B , 1996 . 54 1880 -1891 . DOI:10.1103/PhysRevB.54.1880http://doi.org/10.1103/PhysRevB.54.1880 .
Vahala, K. Optical Microcavities (World Scientific, 2004).
Chang, R. K. & Campillo, A. J. Optical Processes in Microcavities (World Scientific, 1996).
B. Bradlyn , 等 . Topological quantum chemistry . Nature , 2017 . 547 298 -305 . DOI:10.1038/nature23268http://doi.org/10.1038/nature23268 .
M. B. de Paz , 等 . Engineering fragile topology in photonic crystals: topological quantum chemistry of light . Phys. Rev. Res. , 2019 . 1 032005 DOI:10.1103/PhysRevResearch.1.032005http://doi.org/10.1103/PhysRevResearch.1.032005 .
A. P. Schnyder , 等 . Classification of topological insulators and superconductors in three spatial dimensions . Phys. Rev. B , 2008 . 78 195125 DOI:10.1103/PhysRevB.78.195125http://doi.org/10.1103/PhysRevB.78.195125 .
J. C. Y. Teo , C. L. Kane . Topological defects and gapless modes in insulators and superconductors . Phys. Rev. B , 2010 . 82 115120 DOI:10.1103/PhysRevB.82.115120http://doi.org/10.1103/PhysRevB.82.115120 .
J. Ahn , 等 . Stiefel–Whitney classes and topological phases in band theory . Chin. Phys. B , 2019 . 28 117101 DOI:10.1088/1674-1056/ab4d3bhttp://doi.org/10.1088/1674-1056/ab4d3b .
Polyanskiy, M. Refractive index database. at https://refractiveindex.infohttps://refractiveindex.info.
Palik, E. D. Handbook of Optical Constants of Solids (Elsevier, 1997).
J. R. de Lasson , 等 . Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities . Opt. Express , 2018 . 26 11366 -11392 . DOI:10.1364/OE.26.011366http://doi.org/10.1364/OE.26.011366 .
J. Asakura , 等 . A numerical method for nonlinear eigenvalue problems using contour integrals . JSIAM Lett. , 2009 . 1 52 -55 . DOI:10.14495/jsiaml.1.52http://doi.org/10.14495/jsiaml.1.52 .
H. Isakari , T. Takahashi , T. Matsumoto . Periodic band structure calculation by the Sakurai–Sugiura method with a fast direct solver for the boundary element method with the fast multipole representation . Eng. Anal. Bound. Elem. , 2016 . 68 42 -53 . DOI:10.1016/j.enganabound.2016.03.018http://doi.org/10.1016/j.enganabound.2016.03.018 .
C. J. Zheng , 等 . An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method . J. Comput. Phys. , 2016 . 305 677 -699 . DOI:10.1016/j.jcp.2015.10.048http://doi.org/10.1016/j.jcp.2015.10.048 .
T. Sakurai , Y. Futamura , H. Tadano . Efficient parameter estimation and implementation of a contour integral-based eigensolver . J. Algorithms Comput. Technol. , 2013 . 7 249 -269 . DOI:10.1260/1748-3018.7.3.249http://doi.org/10.1260/1748-3018.7.3.249 .
H. F. Gao , 等 . Eigenvalue analysis for acoustic problem in 3d by boundary element method with the block Sakurai–Sugiura method . Eng. Anal. Bound. Elem. , 2013 . 37 914 -923 . DOI:10.1016/j.enganabound.2013.03.015http://doi.org/10.1016/j.enganabound.2013.03.015 .
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