Journals Articles Conferences News About CLP
Submit a paper Email Alert
Search
Search
Articles
Journals
News
Advanced Search
Top Searches
2D MaterialsTransformation opticsQuantum PhotonicsSmall lasersSemiconductor UV PhotonicsSupersymmetric microring laser arrays

Acta Optica Sinica (Online), Volume. 2, Issue 8, 0810001(2025)

Progress in Non-Abelian Band Topology in Photonics (Invited)

Changze Li1...2,3, Zhanshan Wang1,2,3, Xinbin Cheng1,2,3, and Tianshu Jiang1,23,* |Show fewer author(s)
Author Affiliations
  • 1Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
  • 2MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai 200092, China
  • 3Shanghai Frontiers Science Center of Digital Optics, Shanghai 200092, China
    • show less
    AbstractGet PDF(in Chinese)
    Figures&Tables (17)
    Equations (0)
    References (69)
    Tools
    Paper Information
    Topics
    References(69)

    [1] Halperin B I. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential[J]. Physical Review B, 25, 2185-2190(1982).

    [2] Thouless D J, Kohmoto M, Nightingale M P et al. Quantized hall conductance in a two-dimensional periodic potential[J]. Physical Review Letters, 49, 405-408(1982).

    [3] Haldane F D. Model for a quantum Hall effect without landau levels: condensed-matter realization of the “parity anomaly”[J]. Physical Review Letters, 61, 2015-2018(1988).

    [4] Qi X L, Zhang S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 83, 1057-1110(2011).

    [5] Kohmoto M. Topological invariant and the quantization of the Hall conductance[J]. Annals of Physics, 160, 343-354(1985).

    [6] Hatsugai Y. Chern number and edge states in the integer quantum Hall effect[J]. Physical Review Letters, 71, 3697-3700(1993).

    [7] Alexander J W. Topological invariants of knots and links[J]. Transactions of the American Mathematical Society, 30, 275-306(1928).

    [8] Schnyder A P, Ryu S, Furusaki A et al. Classification of topological insulators and superconductors in three spatial dimensions[J]. Physical Review B, 78, 195125(2008).

    [9] King-Smith R D, Vanderbilt D. Theory of polarization of crystalline solids[J]. Physical Review B, 47, 1651-1654(1993).

    [10] Rhim J W, Behrends J, Bardarson J H. Bulk-boundary correspondence from the intercellular Zak phase[J]. Physical Review B, 95, 035421(2017).

    [11] Wu Q S, Soluyanov A A, Bzdušek T. Non-Abelian band topology in noninteracting metals[J]. Science, 365, 1273-1277(2019).

    [12] Yang Y, Yang B, Ma G C et al. Non-Abelian physics in light and sound[J]. Science, 383, eadf9621(2024).

    [13] Guo Q H, Jiang T S, Zhang R Y et al. Experimental observation of non-Abelian topological charges and edge states[J]. Nature, 594, 195-200(2021).

    [14] Jiang T S, Guo Q H, Zhang R Y et al. Four-band non-Abelian topological insulator and its experimental realization[J]. Nature Communications, 12, 6471(2021).

    [15] Li T Y, Hu H P. Floquet non-Abelian topological insulator and multifold bulk-edge correspondence[J]. Nature Communications, 14, 6418(2023).

    [16] Sun X C, Wang J B, He C et al. Non-Abelian topological phases and their quotient relations in acoustic systems[J]. Physical Review Letters, 132, 216602(2024).

    [17] Jiang T S, Zhang R Y, Guo Q H et al. Two-dimensional non-Abelian topological insulators and the corresponding edge/corner states from an eigenvector frame rotation perspective[J]. Physical Review B, 106, 235428(2022).

    [18] Ezawa M. Non-Hermitian non-Abelian topological insulators with PT symmetry[J]. Physical Review Research, 3, 043006(2021).

    [19] Liang Y M, Wang R, Yu Z Z et al. Three-band non-Hermitian non-Abelian topological insulator with PT symmetry[J]. Physical Review B, 109, 115127(2024).

    [20] Tiwari A, Bzdušek T. Non-Abelian topology of nodal-line rings in PT-symmetric systems[J]. Physical Review B, 101, 195130(2020).

    [21] Lenggenhager P M, Liu X X, Tsirkin S S et al. From triple-point materials to multiband nodal links[J]. Physical Review B, 103, L121101(2021).

    [22] Wang M D, Liu S, Ma Q Y et al. Experimental observation of non-Abelian earring nodal links in phononic crystals[J]. Physical Review Letters, 128, 246601(2022).

    [23] Wang D Y, Yang B, Wang M D et al. Observation of non-Abelian charged nodes linking nonadjacent gaps[J]. Physical Review Letters, 129, 263604(2022).

    [24] Wang D Y, Wu Y, Zhang Z Q et al. Non-Abelian frame charge flow in photonic media[J]. Physical Review X, 13, 021024(2023).

    [25] Yang E C, Yang B, You O B et al. Observation of non-Abelian nodal links in photonics[J]. Physical Review Letters, 125, 033901(2020).

    [26] Park H, Wong S, Bouhon A et al. Topological phase transitions of non-Abelian charged nodal lines in spring-mass systems[J]. Physical Review B, 105, 214108(2022).

    [27] Park H, Jones A, Kim M et al. Topological phase transition and surface states in a non-Abelian charged nodal line photonic crystal[J]. Nanophotonics, 13, 1079-1089(2024).

    [28] Bouhon A, Wu Q S, Slager R J et al. Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe[J]. Nature Physics, 16, 1137-1143(2020).

    [29] Yan Q H, Liu R J, Yan Z B et al. Experimental discovery of nodal chains[J]. Nature Physics, 14, 461-464(2018).

    [30] Park H, Wong S, Zhang X et al. Non-Abelian charged nodal links in a dielectric photonic crystal[J]. ACS Photonics, 8, 2746-2754(2021).

    [31] Park H, Gao W L, Zhang X et al. Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems[J]. Nanophotonics, 11, 2779-2801(2022).

    [32] Guo C X, Chen S, Ding K et al. Exceptional non-Abelian topology in multiband non-Hermitian systems[J]. Physical Review Letters, 130, 157201(2023).

    [33] Ahn J, Park S, Yang B J. Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle[J]. Physical Review X, 9, 021013(2019).

    [34] Kang J, Vafek O. Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic-angle twisted bilayer graphene[J]. Physical Review B, 102, 035161(2020).

    [35] Jiang B, Bouhon A, Lin Z K et al. Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions[J]. Nature Physics, 17, 1239-1246(2021).

    [36] Qiu H H, Zhang Q C, Liu T Z et al. Minimal non-Abelian nodal braiding in ideal metamaterials[J]. Nature Communications, 14, 1261(2023).

    [37] Hu Y Z, Tong M Y, Jiang T et al. Observation of two-dimensional time-reversal broken non-Abelian topological states[J]. Nature Communications, 15, 10036(2024).

    [38] Slager R J, Bouhon A, Nur Ünal F. Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems[J]. Nature Communications, 15, 1144(2024).

    [39] Peng B, Bouhon A, Monserrat B et al. Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates[J]. Nature Communications, 13, 423(2022).

    [40] Peng B, Bouhon A, Slager R J et al. Multigap topology and non-Abelian braiding of phonons from first principles[J]. Physical Review B, 105, 085115(2022).

    [41] Breach O, Slager R J, Nur Ünal F. Interferometry of non-Abelian band singularities and Euler class topology[J]. Physical Review Letters, 133, 093404(2024).

    [42] Chen S Y, Bouhon A, Slager R J et al. Non-Abelian braiding of Weyl nodes via symmetry-constrained phase transitions[J]. Physical Review B, 105, L081117(2022).

    [43] Ahn J, Kim D, Kim Y et al. Band topology and linking structure of nodal line semimetals with Z2 monopole charges[J]. Physical Review Letters, 121, 106403(2018).

    [44] Bzdušek T, Sigrist M. Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems[J]. Physical Review B, 96, 155105(2017).

    [45] Zhao Y, Lu Y. PT-symmetric real Dirac fermions and semimetals[J]. Physical Review Letters, 118, 056401(2017).

    [46] Lenggenhager P M, Liu X X, Neupert T et al. Universal higher-order bulk-boundary correspondence of triple nodal points[J]. Physical Review B, 106, 085129(2022).

    [47] Park S, Hwang Y, Choi H C et al. Topological acoustic triple point[J]. Nature Communications, 12, 6781(2021).

    [48] Ünal F N, Bouhon A, Slager R J. Topological Euler class as a dynamical observable in optical lattices[J]. Physical Review Letters, 125, 053601(2020).

    [49] Ezawa M. Topological Euler insulators and their electric circuit realization[J]. Physical Review B, 103, 205303(2021).

    [50] Jiang B, Bouhon A, Wu S Q et al. Observation of an acoustic topological Euler insulator with meronic waves[J]. Science Bulletin, 69, 1653-1659(2024).

    [51] Jankowski W J, Morris A S, Davoyan Z et al. Non-Abelian Hopf-Euler insulators[J]. Physical Review B, 110, 075135(2024).

    [52] Lange G F, Bouhon A, Monserrat B et al. Topological continuum charges of acoustic phonons in two dimensions and the Nambu-Goldstone theorem[J]. Physical Review B, 105, 064301(2022).

    [53] Sun X Q, Zhang S C, Bzdušek T. Conversion rules for Weyl points and nodal lines in topological media[J]. Physical Review Letters, 121, 106402(2018).

    [54] Ding K, Fang C, Ma G C. Non-Hermitian topology and exceptional-point geometries[J]. Nature Reviews Physics, 4, 745-760(2022).

    [55] Chen Y T, Zhang R Y, Xiong Z F et al. Non-Abelian gauge field optics[J]. Nature Communications, 10, 3125(2019).

    [56] Liu B B, Xu T, Hang Z H. A general recipe to observe non-Abelian gauge field in metamaterials[EB/OL]. https://www.degruyter.com/document/doi/10.1515/nanoph-2024-0414/html

    [57] Yang Y, Peng C, Zhu D et al. Synthesis and observation of non-Abelian gauge fields in real space[J]. Science, 365, 1021-1025(2019).

    [58] Whittaker C E, Dowling T, Nalitov A V et al. Optical analogue of Dresselhaus spin-orbit interaction in photonic graphene[J]. Nature Photonics, 15, 193-196(2021).

    [59] Polimeno L, Fieramosca A, Lerario G et al. Experimental investigation of a non-Abelian gauge field in 2D perovskite photonic platform[J]. Optica, 8, 1442-1447(2021).

    [60] Cheng D L, Wang K, Fan S H. Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension[J]. Physical Review Letters, 130, 083601(2023).

    [61] Liang Q, Dong Z L, Pan J S et al. Chiral dynamics of ultracold atoms under a tunable SU(2) synthetic gauge field[J]. Nature Physics, 20, 1738-1743(2024).

    [62] Cheng D L, Wang K, Roques-Carmes C et al. Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions[J]. Nature, 637, 52-56(2025).

    [63] Yan Q C, Wang Z H, Wang D Y et al. Non-Abelian gauge field in optics[J]. Advances in Optics and Photonics, 15, 907-976(2023).

    [64] Liu V, Yang Y, Joannopoulos J D et al. Three-dimensional non-Abelian generalizations of the hofstadter model: spin-orbit-coupled butterfly trios[J]. Physical Review B, 104, 115127(2021).

    [65] Wu J X, Wang Z, Biao Y C et al. Non-Abelian gauge fields in circuit systems[J]. Nature Electronics, 5, 635-642(2022).

    [66] Yang Y, Po H C, Liu V et al. Non-Abelian nonsymmorphic chiral symmetries[J]. Physical Review B, 106, L161108(2022).

    [67] Cheng D L, Wang K, Fan S H. Artificial synthesis of non-Abelian lattice gauge fields in the photonic synthetic frequency dimension[C], FTu3D.7(2023).

    [68] Fumeron S, Berche B. Introduction to topological defects: from liquid crystals to particle physics[J]. The European Physical Journal Special Topics, 232, 1813-1833(2023).

    [69] Mermin N D. The topological theory of defects in ordered media[J]. Reviews of Modern Physics, 51, 591-648(1979).

    Tools

    Get Citation

    Copy Citation Text

    Changze Li, Zhanshan Wang, Xinbin Cheng, Tianshu Jiang. Progress in Non-Abelian Band Topology in Photonics (Invited)[J]. Acta Optica Sinica (Online), 2025, 2(8): 0810001

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Set citation alerts for article
    Save article for my favorites
    Paper Information

    Category: Topological Photonics

    Received: Dec. 16, 2024

    Accepted: Feb. 10, 2025

    Published Online: Apr. 10, 2025

    The Author Email: Jiang Tianshu (tsjiang@tongji.edu.cn)

    DOI:10.3788/AOSOL240473

    CSTR:32394.14.AOSOL240473

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology