Volume 14 Issue 4
Jul.  2021
Turn off MathJax
Article Contents
LIU Shuo, ZHANG Shuang, CUI Tie-jun. Topological circuit: a playground for exotic topological physics[J]. Chinese Optics, 2021, 14(4): 736-753. doi: 10.37188/CO.2021-0095
Citation: LIU Shuo, ZHANG Shuang, CUI Tie-jun. Topological circuit: a playground for exotic topological physics[J]. Chinese Optics, 2021, 14(4): 736-753. doi: 10.37188/CO.2021-0095

Topological circuit: a playground for exotic topological physics

doi: 10.37188/CO.2021-0095
Funds:  Supported by European Union′s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie (No. 833797); Royal Society, the Wolfson Foundation, Horizon 2020 Action Project (No. 734578, D-SPA; 648783, Topological); National key Research and Development Program of China (No. 2017YFA0700201, No. 2017YFA0700202, No. 2017YFA0700203); National Natural Science Foundation of China (No. 61631007, No. 61571117, No. 61875133, No. 11874269); Part by the 111 Project (No. 111-2-05)
More Information
  • Author Bio:

    刘 硕(1988—),男,河北赞皇人,博士,伯明翰大学天文与物理学院玛丽居里学者,2017年于东南大学获得博士学位,主要从事信息超材料、电路拓扑绝缘体的理论与实验方面的研究工作。E-mail:liushuo.china@seu.edu.cn

    张 霜(1975—),男,辽宁大连人,香港大学物理系和电子工程系讲座教授,2005年于美国新墨西哥大学电子工程系获得博士学位,2016年当选美国光学学会会士。在超构材料领域作出了很多重要成果。首次在光学波段实现了负折射率材料、首次通过贝里相位实现了谐波产生的非线性系数的连续控制、首次提出了有效介质(超构材料)的光学拓扑现象、首次实现了理想外尔点并实验上观测到光学系统的朗道手性零级模式、提出了等离激元结构的电磁诱导透明、首次实现了可见光波段宏观尺度的隐身斗篷等。2010年获国际物理联合会的青年科学家光学奖,2016年获英国皇家学会的Wolfson 科研奖。2018−2020连续三年入选科睿唯安全球“高被引科学家”名录。共发表论文200余篇,论文总被引用次数26000余次(谷歌学术)。E-mail:shuzhang@hku.hk

    崔铁军(1965—),男,河北承德人,计算电磁学和电磁超材料专家,中国科学院院士,东南大学首席教授,IEEE Fellow。长期从事电磁超材料和计算电磁学研究,创造性地提出从信息科学角度研究超材料的思想,提出数字编码和可编程超材料及其控制电磁波的新方法,创建了信息超材料新体系;提出了电磁波与复杂目标及环境相互作用的一系列高效算法,开发了具有自主知识产权的系列专用电磁仿真软件;在中国航天、航空、电子和船舶等工业部门进行了大量应用,取得了显著的经济效益与社会效益。发表学术论文500余篇,被引用37000余次(H因子95)。研究成果入选2010年中国科学十大进展、2016年中国光学重要成果;获2011年教育部自然科学一等奖、2014年国家自然科学二等奖、2016年军队科学技术进步一等奖、2018年国家自然科学二等奖。E-mail:tjcui@seu.edu.cn

  • Corresponding author: zhangs75@gmail.comTjcui@seu.edu.cn
  • Received Date: 29 Apr 2021
  • Rev Recd Date: 08 Jun 2021
  • Available Online: 22 Jun 2021
  • Publish Date: 01 Jul 2021
  • Exploring topological phases of matter and their exotic physics appeared as a rapidly growing field of study in solid-state electron systems in the past decade. In recent years, there has been a trend on the emulation of topological insulators/semimetals in many other systems, including ultracold quantum gases, trapped ions, photonic, acoustic, mechanical, and electrical circuit systems. Among these platforms, topological circuits made of simple capacitive and inductive circuit elements emerged as a very competitive platform because of its highly controllable degrees of freedom, lowercost, easy implementation, and great flexibility for integration. Owing to the unique advantages of electrical circuits such as arbitrary engineering of long-range hopping, convenient realization of nonlinear, nonreciprocal, and gain effects, highly flexible measurement, many of the nonlinear, non-abelian, and non-Hermitian physics can be potentially realized and investigated using the electrical circuit platform. In this review, we provide the first short overview of the main achievements of topological circuits developed in the past six years, primarily focusing on their theoretical modeling, circuit construction, experimental characterization, and their distinction from their counterparts in quantum electronics and photonics. The scope of this review covers a wide variety of topological circuits, including Hermitian topological circuits hosting nontrivial edge state, higher-order corner state, Weyl particles; higher dimensional topological circuits exhibiting nodal link and nodal knot states; non-Hermitian topological circuits showing skin effects, gain and loss induced nontrivial edge state; self-induced topological edge state in nonlinear topological circuit; topological circuit having non-Abelian gauge potential.

     

  • loading
  • [1]
    HASAN M Z, KANE C L. Colloquium: topological insulators[J]. Reviews of Modern Physics, 2010, 82(4): 3045-3067. doi: 10.1103/RevModPhys.82.3045
    [2]
    QI X L, ZHANG SH CH. Topological insulators and superconductors[J]. Reviews of Modern Physics, 2011, 83(4): 1057-1110. doi: 10.1103/RevModPhys.83.1057
    [3]
    BERNEVIG B A, HUGHES T L. Topological Insulators and Topological Superconductors[M]. Princeton: Princeton University Press, 2013.
    [4]
    HUGHES T L. Photonic topological insulators[B]. Taylor L. Hughes, 2013.
    [5]
    LU L, JOANNOPOULOS J D, SOLJAČIĆ M. Topological photonics[J]. Nature Photonics, 2014, 8(11): 821-829. doi: 10.1038/nphoton.2014.248
    [6]
    MA G C, XIAO M, CHAN C T. Topological phases in acoustic and mechanical systems[J]. Nature Reviews Physics, 2019, 1(4): 281-294. doi: 10.1038/s42254-019-0030-x
    [7]
    DONG J K, JURICIC V, ROY B. Topolectric circuits: theory and construction[J]. arXiv preprint arXiv: 2008.11202, 2020.
    [8]
    LU L. Topology on a breadboard[J]. Nature Physics, 2018, 14(9): 875-877. doi: 10.1038/s41567-018-0235-4
    [9]
    JIA N Y, OWENS C, SOMMER A, et al. Time- and site-resolved dynamics in a topological circuit[J]. Physical Review X, 2015, 5(2): 021031. doi: 10.1103/PhysRevX.5.021031
    [10]
    LEE C H, IMHOF S, BERGER C, et al. Topolectrical circuits[J]. Communications Physics, 2018, 1: 39. doi: 10.1038/s42005-018-0035-2
    [11]
    HOFMANN T, HELBIG T, LEE C H, et al. Chiral voltage propagation and calibration in a topolectrical chern circuit[J]. Physical Review Letters, 2019, 122(24): 247702. doi: 10.1103/PhysRevLett.122.247702
    [12]
    ZHAO E H. Topological circuits of inductors and capacitors[J]. Annals of Physics, 2018, 399: 289-313. doi: 10.1016/j.aop.2018.10.006
    [13]
    LIU SH, SHAO R W, MA SH J, et al. Non-Hermitian skin effect in a non-Hermitian electrical circuit[J]. Research, 2021, 2021: 5608038.
    [14]
    PETERSON C W, BENALCAZAR W A, HUGHES T L, et al. A quantized microwave quadrupole insulator with topologically protected corner states[J]. Nature, 2018, 555(7696): 346-350. doi: 10.1038/nature25777
    [15]
    LU Y H, JIA N Y, SU L, et al. Probing the berry curvature and Fermi arcs of a Weyl circuit[J]. Physical Review B, 2019, 99(2): 020302. doi: 10.1103/PhysRevB.99.020302
    [16]
    LUO K F, YU R, WENG H M. Topological nodal states in circuit lattice[J]. Research, 2018, 2018: 6793752.
    [17]
    LIU SH, GAO W L, ZHANG Q, et al. Topologically protected edge state in two-dimensional Su–Schrieffer–Heeger Circuit[J]. Research, 2019, 2019: 8609875.
    [18]
    XU S Y, BELOPOLSKI I, ALIDOUST N, et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs[J]. Science, 2015, 349(6248): 613-617. doi: 10.1126/science.aaa9297
    [19]
    HUANG L N, MCCORMICK T M, OCHI M, et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2[J]. Nature Materials, 2016, 15(11): 1155-1160. doi: 10.1038/nmat4685
    [20]
    LU L, WANG ZH Y, YE D X, et al. Experimental observation of Weyl points[J]. Science, 2015, 349(6248): 622-624. doi: 10.1126/science.aaa9273
    [21]
    YANG B, GUO Q H, TREMAIN B, et al. Ideal Weyl points and helicoid surface states in artificial photonic crystal structures[J]. Science, 2018, 359(6379): 1013-1016. doi: 10.1126/science.aaq1221
    [22]
    OWENS C, LACHAPELLE A, SAXBERG B, et al. Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array[J]. Physical Review A, 2018, 97(1): 013818. doi: 10.1103/PhysRevA.97.013818
    [23]
    LI R J, LV B, TAO H B, et al. Ideal type-II Weyl points in topological circuits[J]. National Science Review, 2020: nwaa192. doi: 10.1093/nsr/nwaa192
    [24]
    SOLUYANOV A A, GRESCH D, WANG ZH J, et al. Type-II Weyl semimetals[J]. Nature, 2015, 527(7579): 495-498. doi: 10.1038/nature15768
    [25]
    JIANG J, LIU Z K, SUN Y, et al. Signature of type-II Weyl semimetal phase in MoTe2[J]. Nature Communications, 2017, 8: 13973. doi: 10.1038/ncomms13973
    [26]
    NOH J, HUANG SH, LEYKAM D, et al. Experimental observation of optical Weyl points and Fermi arc-like surface states[J]. Nature Physics, 2017, 13(6): 611-617. doi: 10.1038/nphys4072
    [27]
    YANG B, GUO Q H, TREMAIN B. Direct observation of topological surface-state arcs in photonic metamaterials[J]. Nature Communications, 2017, 8: 97. doi: 10.1038/s41467-017-00134-1
    [28]
    RAFI-UL-ISLAM SM, SIU BZ, SUN CH, et al. Realization of Weyl semimetal phases in topoelectrical circuits[J]. New Journal of Physics, 2020, 22: 023025. doi: 10.1088/1367-2630/ab6eaf
    [29]
    RAFI-UI-ISLAM SM, SIU Z B, JALI L M. Topoelectrical circuit realization of a Weyl semimetal heterojunction[J]. Communication Physics, 2020, 3: 72.
    [30]
    BENALCAZAR W A, BERNEVIG B A, HUGHES T L. Quantized electric multipole insulators[J]. Science, 2017, 357(6346): 61-66. doi: 10.1126/science.aah6442
    [31]
    LANGBEHN J, PENG Y, TRIFUNOVIC L, et al. Reflection-symmetric second-order topological insulators and superconductors[J]. Physical Review Letters, 2017, 119(24): 246401. doi: 10.1103/PhysRevLett.119.246401
    [32]
    KHALAF E. Higher-order topological insulators and superconductors protected by inversion symmetry[J]. Physical Review B, 2018, 97(20): 205136. doi: 10.1103/PhysRevB.97.205136
    [33]
    IMHOF S, BERGER C, BAYER F, et al. Topoelectrical-circuit realization of topological corner modes[J]. Nature Physics, 2018, 14(9): 925-929. doi: 10.1038/s41567-018-0246-1
    [34]
    LIU SH, MA SH J, ZHANG L, et al. Octupole corner state in a three-dimensional topological circuit[J]. Light:Science &Applications, 2020, 9: 145.
    [35]
    BAO J CH, ZOU D Y, ZHANG W X, et al. Topoelectrical circuit octupole insulator with topologically protected corner states[J]. Physical Review B, 2019, 100(200): 201406.
    [36]
    EZAWA M. Braiding of Majorana-like corner states in electric circuits and its non-Hermitian generalization[J]. Physical Review B, 2019, 100(4): 045407. doi: 10.1103/PhysRevB.100.045407
    [37]
    CHIU C K, TEO J C Y, SCHNYDER A P, et al. Classification of topological quantum matter with symmetries[J]. Review Modern Physics, 2016, 88(3): 035005. doi: 10.1103/RevModPhys.88.035005
    [38]
    PRICE H M, ZILBERBERG O, OZAWA T, et al. Four-dimensional quantum hall effect with ultracold atoms[J]. Physical Review Letters, 2015, 115(19): 195303. doi: 10.1103/PhysRevLett.115.195303
    [39]
    OZAWA T, PRICE H M, GOLDMAN N, et al. Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics[J]. Physical Review A, 2016, 93(4): 043827. doi: 10.1103/PhysRevA.93.043827
    [40]
    WANG Y, PRICE H M, ZHANG B L, et al. Circuit implementation of a four-dimensional topological insulator[J]. Nature Communications, 2020, 11: 2356. doi: 10.1038/s41467-020-15940-3
    [41]
    LI L H, LEE C H, GONG J B. Boundary states of 4D topological matter: emergence and full 3D-imaging of nodal Seifert surfaces[J]. Communications Physics, 2019, 2: 135. doi: 10.1038/s42005-019-0235-4
    [42]
    TAKATA K, NOTOMI M. Photonic topological insulating phase induced solely by gain and loss[J]. Physical Review Letters, 2018, 121(21): 213902. doi: 10.1103/PhysRevLett.121.213902
    [43]
    YAO SH Y, WANG ZH. Edge states and topological invariants of non-hermitian systems[J]. Physical Review Letters, 2018, 121(8): 086803. doi: 10.1103/PhysRevLett.121.086803
    [44]
    SHEN H T, ZHEN B, FU L. Topological band theory for non-Hermitian Hamiltonians[J]. Physical Review Letters, 2018, 120(14): 146402. doi: 10.1103/PhysRevLett.120.146402
    [45]
    KAWABATA K, HIGASHIKAWA S, GONG Z P, et al. Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics[J]. Nature Communications, 2019, 10: 297. doi: 10.1038/s41467-018-08254-y
    [46]
    YAO SH Y, SONG F, WANG ZH. Non-hermitian chern bands[J]. Physical Review Letters, 2018, 121(12): 136802.
    [47]
    YOKOMIZO K, MURAKAMI S. Non-bloch band theory of non-Hermitian systems[J]. Physical Review Letters, 2019, 123(6): 066404. doi: 10.1103/PhysRevLett.123.066404
    [48]
    LIU SH, MA SH J, YANG CH, et al. Gain-and loss-induced topological insulating phase in a non-Hermitian electrical circuit[J]. Physical Review Applied, 2020, 13(1): 014047. doi: 10.1103/PhysRevApplied.13.014047
    [49]
    HELBIG T, HOFMANN T, IMHOF M, et al. Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits[J]. Nature Physics, 2020, 16(7): 747-750. doi: 10.1038/s41567-020-0922-9
    [50]
    EZAWA M. Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits[J]. Physical Review B, 2019, 99(12): 121411. doi: 10.1103/PhysRevB.99.121411
    [51]
    EZAWA M. Electric circuits for non-Hermitian Chern insulators[J]. Physical Review B, 2019, 100(8): 081401. doi: 10.1103/PhysRevB.100.081401
    [52]
    LUO K F, FENG J J, ZHAO Y X, et al.. Nodal manifolds bounded by exceptional points on non-hermitian honeycomb lattices and electrical-circuit realizations[J]. arXiv preprint arXiv: 1810.09231, 2018.
    [53]
    WU Q SH, SOLUYANOV A A, BZDUŠEK T. Non-Abelian band topology in noninteracting metals[J]. Science, 2019, 365(6459): 1273-1277. doi: 10.1126/science.aau8740
    [54]
    TIWARI A, BZDUŠEK T. Non-Abelian topology of nodal-line rings in PT-symmetric systems[J]. Physical Review B, 2020, 101(19): 195130. doi: 10.1103/PhysRevB.101.195130
    [55]
    YANG E CH, YANG B, YOU O B, et al. Observation of non-Abelian nodal links in photonics[J]. Physical Review Letters, 2020, 125(3): 033901. doi: 10.1103/PhysRevLett.125.033901
    [56]
    JACOB A, ÖHBERG P, JUZELIŪNAS G, et al. Cold atom dynamics in non-Abelian gauge fields[J]. Applied Physics B, 2007, 89(4): 439-445. doi: 10.1007/s00340-007-2865-6
    [57]
    STERN A, LINDNER N H. Topological quantum computation—from basic concepts to first experiments[J]. Science, 2013, 339(6124): 1179-1184. doi: 10.1126/science.1231473
    [58]
    WU ZH, ZHANG L, SUN W, et al. Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates[J]. Science, 2016, 354(6308): 83-88. doi: 10.1126/science.aaf6689
    [59]
    CHEN Y T, ZHANG R Y, XIONG ZH F, et al. Non-Abelian gauge field optics[J]. Nature Communications, 2019, 10: 3125. doi: 10.1038/s41467-019-10974-8
    [60]
    YANG Y, PENG CH, ZHU D, et al. Synthesis and observation of non-Abelian gauge fields in real space[J]. Science, 2019, 365(6457): 1021-1025. doi: 10.1126/science.aay3183
    [61]
    RECHCIŃSKA K, KRÓL M, MAZUR R, et al. Engineering spin-orbit synthetic Hamiltonians in liquid-crystal optical cavities[J]. Science, 2019, 366(6466): 727-730. doi: 10.1126/science.aay4182
    [62]
    GIANFRATE A, BLEU O, DOMINICI L, et al. Measurement of the quantum geometric tensor and of the anomalous Hall drift[J]. Nature, 2020, 578(7795): 381-385. doi: 10.1038/s41586-020-1989-2
    [63]
    GUO Q H, JIANG T SH, ZHANG R Y, et al.. Experimental observation of non-Abelian topological charges and bulk-edge correspondence[J]. arXiv preprint arXiv: 2008.06100, 2020.
    [64]
    SONG Z Y, WU T Y, WU W Q, et al.. Experimental realization of non-Abelian gauge potentials and topological Chern state in circuit system[J]. arXiv preprint arXiv: 2009.04870, 2020.
    [65]
    DRESSELHAUS G. Spin-orbit coupling effects in zinc blende structures[J]. Physical Review, 1955, 100(2): 580-586. doi: 10.1103/PhysRev.100.580
    [66]
    EZAWA M. Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits[J]. Physical Review B, 2020, 102(7): 075424. doi: 10.1103/PhysRevB.102.075424
    [67]
    NAYAK C, SIMON S H, STERN A, et al. Non-Abelian anyons and topological quantum computation[J]. Reviews of Modern Physics, 2008, 80(3): 1083-1159. doi: 10.1103/RevModPhys.80.1083
    [68]
    HADAD Y, SORIC J C, KHANIKAEV A B, et al. Self-induced topological protection in nonlinear circuit arrays[J]. Nature Electronics, 2018, 1(3): 178-182. doi: 10.1038/s41928-018-0042-z
    [69]
    HADAD Y, VITELLI V, ALU A, et al. Solitons and propagating domain walls in topological resonator arrays[J]. ACS Photonics, 2017, 4(8): 1974-1979. doi: 10.1021/acsphotonics.7b00303
    [70]
    WANG Y, LANG L J, LEE C H, et al. Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial[J]. Nature Communications, 2019, 10: 1102. doi: 10.1038/s41467-019-08966-9
    [71]
    HIROTA R, SUZUKI K. Theoretical and experimental studies of lattice solitons in nonlinear lumped networks[J]. Proceedings of the IEEE, 1973, 61(10): 1483-1491. doi: 10.1109/PROC.1973.9297
    [72]
    NAGASHIMA H, AMAGISHI Y. Experiment on solitons in the dissipative Toda lattice using nonlinear transmission line[J]. Journal of the Physical Society of Japan, 1979, 47(6): 2021-2027. doi: 10.1143/JPSJ.47.2021
    [73]
    MUROYA K, WATANABE S. Experiment on soliton in inhomogeneous electric circuit. I. Dissipative case[J]. Journal of the Physical Society of Japan, 1981, 50(9): 3159-3165. doi: 10.1143/JPSJ.50.3159
    [74]
    MUROYA K, SAITOH N, WATANABE S. Experiment on lattice soliton by nonlinear LC Circuit—observation of a dark soliton[J]. Journal of the Physical Society of Japan, 1982, 51(3): 1024-1029. doi: 10.1143/JPSJ.51.1024
    [75]
    KUUSELA T, HIETARINTA J, KOKKO K, et al. Soliton experiments in a nonlinear electrical transmission line[J]. European Journal of Physics, 1987, 8(1): 27-33. doi: 10.1088/0143-0807/8/1/007
    [76]
    LEE C H, SUTRISNO A, HOFMANN T, et al. Imaging nodal knots in momentum space through topolectrical circuits[J]. Nature Communications, 2020, 11: 4385. doi: 10.1038/s41467-020-17716-1
    [77]
    ZHANG W X, ZOU D Y, BAO J CH, et al. Topolectrical-circuit realization of a four-dimensional hexadecapole insulator[J]. Physical Review B, 2020, 102(10): 100102. doi: 10.1103/PhysRevB.102.100102
    [78]
    HOFMANN T, HELBIG T, SCHINDLER F, et al. Reciprocal skin effect and its realization in a topolectrical circuit[J]. Physical Review Research, 2020, 2(2): 023265. doi: 10.1103/PhysRevResearch.2.023265
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(7)

    Article views(1659) PDF downloads(335) Cited by()
    Proportional views

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return