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Intrinsic topological hinge states induced by boundary gauge fields in photonic metamaterials
- Affiliations：
- Author bio：
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DOI：10.1186/s43593-025-00097-7
CLC：Received：20 March 2025，
Revised：2025-06-04，
Accepted：28 June 2025，
Published Online：15 August 2025，
Published：2025-12
- Accepted：
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Changsheng He, Liang Zhao, Shuang Zhang, et al. Intrinsic topological hinge states induced by boundary gauge fields in photonic metamaterials[J]. eLight, 2025, 5.
Changsheng He, Liang Zhao, Shuang Zhang, et al. Intrinsic topological hinge states induced by boundary gauge fields in photonic metamaterials[J]. eLight, 2025, 5. DOI： 10.1186/s43593-025-00097-7.
摘要
Abstract
Higher-order topological insulators (HOTIs) can support boundary states at least two dimensions lower than the bulk
attracting intensive attention from both fundamental science and application sides. Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems. Here
beyond lattice model
we dem
onstrate that a cylinder with an arbitrary cross section
composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers
<math id="IEq1_Math"><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>=</mo><mo>±</mo><mn>1</mn></mrow></math>
$$${c}_{2}=\pm 1$$$
in a synthetic five-dimensional space
can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space. Interestingly
this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states
guaranteed by a nontrivial
<math id="IEq2_Math"><msub><mi>c</mi><mn>2</mn></msub></math>
$$${c}_{2}$$$
and an effective magnetic field induced by the curvature of the cylinder surface. Compared to conventional schemes to generate HOTIs
our approach is more robust
as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal
parity
or chi
ral symmetry. We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements. Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space
<math id="IEq3_Math"><msub><mi>c</mi><mn>2</mn></msub></math>
$$${c}_{2}$$$
and real-space HOTI states
thereby generalizing HOTIs to corner-less systems.
关键词
Keywords
references
X.L. Qi , S.C. Zhang , Topological insulators and superconductors . Rev. Mod. Phys. 83 , 1057 - 1110 ( 2011 ). http://doi.org/10.1103/RevModPhys.83.1057 http://doi.org/10.1103/RevModPhys.83.1057
M.Z. Hasan , C.L. Kane , Colloquium: topological insulators . Rev. Mod. Phys. 82 , 3045 - 3067 ( 2010 ). http://doi.org/10.1103/RevModPhys.82.3045 http://doi.org/10.1103/RevModPhys.82.3045
T. Ozawa et al. , Topological photonics . Rev. Mod. Phys. 91 ,( 2019 ). http://doi.org/10.1103/RevModPhys.91.015006 http://doi.org/10.1103/RevModPhys.91.015006
L. Lu , J.D. Joannopoulos , M. Soljačić , Topological photonics . Nat. Photonics 8 , 821 - 829 ( 2014 ). http://doi.org/10.1038/nphoton.2014.248 http://doi.org/10.1038/nphoton.2014.248
L. Lu , J.D. Joannopoulos , M. Soljačić , Topological states in photonic systems . Nat. Phys. 12 , 626 - 629 ( 2016 ). http://doi.org/10.1038/nphys3796 http://doi.org/10.1038/nphys3796
W.A. Benalcazar , B.A. Bernevig , T.L. Hughes , Quantized electric multipole insulators . Science 357 , 61 - 66 ( 2017 ). http://doi.org/10.1126/science.aah6442 http://doi.org/10.1126/science.aah6442
W.A. Benalcazar , B.A. Bernevig , T.L. Hughes , Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators . Phys. Rev. B 96 ,( 2017 ). http://doi.org/10.1103/PhysRevB.96.245115 http://doi.org/10.1103/PhysRevB.96.245115
Z. Song , Z. Fang , C. Fang , (d−2)-Dimensional edge states of rotation symmetry protected topological states . Phys. Rev. Lett. 119 ,( 2017 ). http://doi.org/10.1103/PhysRevLett.119.246402 http://doi.org/10.1103/PhysRevLett.119.246402
F. Schindler et al. , Higher-order topological insulators . Sci. Adv. 4 , eaat0346 ( 2018 ). http://doi.org/10.1126/sciadv.aat0346 http://doi.org/10.1126/sciadv.aat0346
C. Fang , L. Fu , New classes of topological crystalline insulators having surface rotation anomaly . Sci. Adv. 5 , eaat2374 ( 2019 ). http://doi.org/10.1126/sciadv.aat2374 http://doi.org/10.1126/sciadv.aat2374
B. Xie et al. , Higher-order band topology . Nat. Rev. Phys. 3 , 520 - 532 ( 2021 ). http://doi.org/10.1038/s42254-021-00323-4 http://doi.org/10.1038/s42254-021-00323-4
X. Zhang et al. , Second-order topology and multidimensional topological transitions in sonic crystals . Nat. Phys. 15 , 582 - 588 ( 2019 ). http://doi.org/10.1038/s41567-019-0472-1 http://doi.org/10.1038/s41567-019-0472-1
Y. Liu et al. , Second-order topological corner states in two-dimensional elastic wave metamaterials with nonsymmorphic symmetries . Mech. Syst. Signal Proc. 198 ,( 2023 ). http://doi.org/10.1016/j.ymssp.2023.110433 http://doi.org/10.1016/j.ymssp.2023.110433
M. Serra-Garcia et al. , Observation of a phononic quadrupole topological insulator . Nature 555 , 342 - 345 ( 2018 ). http://doi.org/10.1038/nature25156 http://doi.org/10.1038/nature25156
H. Xue , Y. Yang , F. Gao , Y. Chong , B. Zhang , Acoustic higher-order topological insulator on a kagome lattice . Nat. Mater. 18 , 108 - 112 ( 2019 ). http://doi.org/10.1038/s41563-018-0251-x http://doi.org/10.1038/s41563-018-0251-x
Z.-K. Lin et al. , Topological Wannier cycles induced by sub-unit-cell artificial gauge flux in a sonic crystal . Nat. Mater. 21 , 430 - 437 ( 2022 ). http://doi.org/10.1038/s41563-022-01200-w http://doi.org/10.1038/s41563-022-01200-w
S. Liu et al. , Octupole corner state in a three-dimensional topological circuit . Light Sci Appl. 9 , 145 ( 2020 ). http://doi.org/10.1038/s41377-020-00381-w http://doi.org/10.1038/s41377-020-00381-w
S. Imhof et al. , Topolectrical-circuit realization of topological corner modes . Nat. Phys. 14 , 925 - 929 ( 2018 ). http://doi.org/10.1038/s41567-018-0246-1 http://doi.org/10.1038/s41567-018-0246-1
C.W. Peterson , W.A. Benalcazar , T.L. Hughes , G. Bahl , A quantized microwave quadrupole insulator with topologically protected corner states . Nature 555 , 346 - 350 ( 2018 ). http://doi.org/10.1038/nature25777 http://doi.org/10.1038/nature25777
Y. Zhang et al. , Realization of photonic p-orbital higher-order topological insulators . eLight 3 , 5 ( 2023 ). http://doi.org/10.1186/s43593-022-00039-7 http://doi.org/10.1186/s43593-022-00039-7
Z. Hu et al. , Topological orbital angular momentum extraction and twofold protection of vortex transport . Nat. Photonics 19 , 162 - 169 ( 2025 ). http://doi.org/10.1038/s41566-024-01564-2 http://doi.org/10.1038/s41566-024-01564-2
X.-D. Chen et al. , Direct observation of corner states in second-order topological photonic crystal slabs . Phys. Rev. Lett. 122 ,( 2019 ). http://doi.org/10.1103/PhysRevLett.122.233902 http://doi.org/10.1103/PhysRevLett.122.233902
B.-Y. Xie et al. , Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals . Phys. Rev. Lett. 122 ,( 2019 ). http://doi.org/10.1103/PhysRevLett.122.233903 http://doi.org/10.1103/PhysRevLett.122.233903
S. Mittal et al. , Photonic quadrupole topological phases . Nat. Photonics 13 , 692 - 696 ( 2019 ). http://doi.org/10.1038/s41566-019-0452-0 http://doi.org/10.1038/s41566-019-0452-0
C.W. Peterson , T. Li , W.A. Benalcazar , T.L. Hughes , G. Bahl , A fractional corner anomaly reveals higher-order topology . Science 368 , 1114 - 1118 ( 2020 ). http://doi.org/10.1126/science.aba7604 http://doi.org/10.1126/science.aba7604
Y. Liu et al. , Bulk-disclination correspondence in topological crystalline insulators . Nature 589 , 381 - 385 ( 2021 ). http://doi.org/10.1038/s41586-020-03125-3 http://doi.org/10.1038/s41586-020-03125-3
C.-P. Liang et al. , Fractional topological numbers at photonic edges and corners . Phys. Rev. Appl. 20 ,( 2023 ). http://doi.org/10.1103/PhysRevApplied.20.034028 http://doi.org/10.1103/PhysRevApplied.20.034028
J.D. Joannopoulos , P.R. Villeneuve , S. Fan , Photonic crystals . Solid State Commun. 102 , 165 - 173 ( 1997 ). http://doi.org/10.1016/S0038-1098(96)00716-8 http://doi.org/10.1016/S0038-1098(96)00716-8
M. Kadic , G.W. Milton , M. van Hecke , M. Wegener , 3D metamaterials . Nat. Rev. Phys. 1 , 198 - 210 ( 2019 ). http://doi.org/10.1038/s42254-018-0018-y http://doi.org/10.1038/s42254-018-0018-y
S. Ma , B. Yang , S. Zhang , Topological photonics in metamaterials . Photonics Insights 1 , R02 ( 2022 ). http://doi.org/10.3788/PI.2022.R02 http://doi.org/10.3788/PI.2022.R02
Y. Yang et al. , Realization of a three-dimensional photonic topological insulator . Nature 565 , 622 - 626 ( 2019 ). http://doi.org/10.1038/s41586-018-0829-0 http://doi.org/10.1038/s41586-018-0829-0
M. Kim et al. , Three-dimensional photonic topological insulator without spin-orbit coupling . Nat. Commun. 13 , 3499 ( 2022 ). http://doi.org/10.1038/s41467-022-30909-0 http://doi.org/10.1038/s41467-022-30909-0
G.-G. Liu et al. , Topological Chern vectors in three-dimensional photonic crystals . Nature 609 , 925 - 930 ( 2022 ). http://doi.org/10.1038/s41586-022-05077-2 http://doi.org/10.1038/s41586-022-05077-2
B. Yang et al. , Ideal Weyl points and helicoid surface states in artificial photonic crystal structures . Science 359 , 1013 - 1016 ( 2018 ). http://doi.org/10.1126/science.aaq1221 http://doi.org/10.1126/science.aaq1221
Y. Yang et al. , Ideal unconventional weyl point in a chiral photonic metamaterial . Phys. Rev. Lett. 125 ,( 2020 ). http://doi.org/10.1103/PhysRevLett.125.143001 http://doi.org/10.1103/PhysRevLett.125.143001
H. Park , W. Gao , X. Zhang , S.S. Oh , Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems . Nanophotonics 11 , 2779 - 2801 ( 2022 ). http://doi.org/10.1515/nanoph-2021-0692 http://doi.org/10.1515/nanoph-2021-0692
W. Gao et al. , Experimental observation of photonic nodal line degeneracies in metacrystals . Nat. Commun. 9 , 950 ( 2018 ). http://doi.org/10.1038/s41467-018-03407-5 http://doi.org/10.1038/s41467-018-03407-5
Q. Yan et al. , Experimental discovery of nodal chains . Nat. Phys. 14 , 461 - 464 ( 2018 ). http://doi.org/10.1038/s41567-017-0041-4 http://doi.org/10.1038/s41567-017-0041-4
Q. Guo et al. , Three dimensional photonic dirac points in metamaterials . Phys. Rev. Lett. 119 ,( 2017 ). http://doi.org/10.1103/PhysRevLett.119.213901 http://doi.org/10.1103/PhysRevLett.119.213901
Q. Guo et al. , Observation of three-dimensional photonic dirac points and spin-polarized surface arcs . Phys. Rev. Lett. 122 ,( 2019 ). http://doi.org/10.1103/PhysRevLett.122.203903 http://doi.org/10.1103/PhysRevLett.122.203903
S. Sugawa , F. Salces-Carcoba , A.R. Perry , Y. Yue , I.B. Spielman , Second chern number of a quantum-simulated non-Abelian Yang monopole . Science 360 , 1429 - 1434 ( 2018 ). http://doi.org/10.1126/science.aam9031 http://doi.org/10.1126/science.aam9031
C.N. Yang , Generalization of Dirac’s monopole to SU2 gauge fields . J. Math. Phys. 19 , 320 - 328 ( 1978 ). http://doi.org/10.1063/1.523506 http://doi.org/10.1063/1.523506
S. Ma et al. , Linked Weyl surfaces and Weyl arcs in photonic metamaterials . Science 373 , 572 - 576 ( 2021 ). http://doi.org/10.1126/science.abi7803 http://doi.org/10.1126/science.abi7803
B. Lian , S.C. Zhang , Five-dimensional generalization of the topological Weyl semimetal . Phys. Rev. B 94 ,( 2016 ). http://doi.org/10.1103/PhysRevB.94.041105 http://doi.org/10.1103/PhysRevB.94.041105
X. Zheng , T. Chen , W. Zhang , H. Sun , X. Zhang , Exploring topological phase transition and Weyl physics in five dimensions with electric circuits . Phys. Rev. Res. 4 ,( 2022 ). http://doi.org/10.1103/PhysRevResearch.4.033203 http://doi.org/10.1103/PhysRevResearch.4.033203
S. Ma et al. , Gauge field induced chiral zero mode in five-dimensional yang monopole metamaterials . Phys. Rev. Lett. 130 ,( 2023 ). http://doi.org/10.1103/PhysRevLett.130.243801 http://doi.org/10.1103/PhysRevLett.130.243801
K. Hashimoto , Y. Matsuo , Universal higher-order topology from a five-dimensional Weyl semimetal: edge topology, edge Hamiltonian, and a nested Wilson loop . Phys. Rev. B 101 ,( 2020 ). http://doi.org/10.1103/PhysRevB.101.245138 http://doi.org/10.1103/PhysRevB.101.245138
K. Hashimoto , X. Wu , T. Kimura , Edge states at an intersection of edges of a topological material . Phys. Rev. B 95 ,( 2017 ). http://doi.org/10.1103/PhysRevB.95.165443 http://doi.org/10.1103/PhysRevB.95.165443
I. Petrides , O. Zilberberg , Higher-order topological insulators, topological pumps and the quantum Hall effect in high dimensions . Phys. Rev. Res. 2 ,( 2020 ). http://doi.org/10.1103/PhysRevResearch.2.022049 http://doi.org/10.1103/PhysRevResearch.2.022049
X.L. Qi , T.L. Hughes , S.C. Zhang , Topological field theory of time-reversal invariant insulators . Phys. Rev. B 78 ,( 2008 ). http://doi.org/10.1103/PhysRevB.78.195424 http://doi.org/10.1103/PhysRevB.78.195424
Y.X. Zhao , S.A. Yang , Index theorem on chiral landau bands for topological fermions . Phys. Rev. Lett. 126 ,( 2021 ). http://doi.org/10.1103/PhysRevLett.126.046401 http://doi.org/10.1103/PhysRevLett.126.046401
V. Lukose , R. Shankar , G. Baskaran , Novel electric field effects on landau levels in graphene . Phys. Rev. Lett. 98 ,( 2007 ). http://doi.org/10.1103/PhysRevLett.98.116802 http://doi.org/10.1103/PhysRevLett.98.116802
A.G. Grushin , J.W.F. Venderbos , A. Vishwanath , R. Ilan , Inhomogeneous weyl and dirac semimetals: transport in axial magnetic fields and fermi arc surface states from pseudo-landau levels . Phys. Rev. X 6 ,( 2016 ).
S. Jia , S.Y. Xu , M.Z. Hasan , Weyl semimetals, fermi arcs and chiral anomalies . Nat. Mater. 15 , 1140 - 1144 ( 2016 ). http://doi.org/10.1038/nmat4787 http://doi.org/10.1038/nmat4787
H. Jia et al. , Observation of chiral zero mode in inhomogeneous three-dimensional Weyl metamaterials . Science 363 , 148 - 151 ( 2019 ). http://doi.org/10.1126/science.aau7707 http://doi.org/10.1126/science.aau7707
V. Peri , M. Serra-Garcia , R. Ilan , S.D. Huber , Axial-field-induced chiral channels in an acoustic Weyl system . Nat. Phys. 15 , 357 - 361 ( 2019 ). http://doi.org/10.1038/s41567-019-0415-x http://doi.org/10.1038/s41567-019-0415-x
C.-K. Chiu , J.C.Y. Teo , A.P. Schnyder , S. Ryu , Classification of topological quantum matter with symmetries . Rev. Mod. Phys. 88 ,( 2016 ). http://doi.org/10.1103/RevModPhys.88.035005 http://doi.org/10.1103/RevModPhys.88.035005
Z. Xiong , W. Chen , Z. Wang , J. Xu , Y. Chen , Finite element modeling of electromagnetic properties in photonic bianisotropic structures . Front. Optoelectr. 14 , 148 - 153 ( 2021 ). http://doi.org/10.1007/s12200-021-1213-5 http://doi.org/10.1007/s12200-021-1213-5
C. Fietz , Y. Urzhumov , G. Shvets , Complex k band diagrams of 3D metamaterial/photonic crystals . Opt. Express 19 , 19027 - 19041 ( 2011 ). http://doi.org/10.1364/OE.19.019027 http://doi.org/10.1364/OE.19.019027
C. Chen et al. , Second-order real nodal-line semimetal in three-dimensional graphdiyne . Phys. Rev. Lett. 128 ,( 2022 ). http://doi.org/10.1103/PhysRevLett.128.026405 http://doi.org/10.1103/PhysRevLett.128.026405
Y. Pan et al. , Real higher-order Weyl photonic crystal . Nat. Commun. 14 , 6636 ( 2023 ). http://doi.org/10.1038/s41467-023-42457-2 http://doi.org/10.1038/s41467-023-42457-2
K. Wang , J.-X. Dai , L.B. Shao , S.A. Yang , Y.X. Zhao , Boundary criticality of PT-invariant topology and second-order nodal-line semimetals . Phys. Rev. Lett. 125 ,( 2020 ). http://doi.org/10.1103/PhysRevLett.125.126403 http://doi.org/10.1103/PhysRevLett.125.126403
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