Abstract
We construct an electrical circuit to realize a modified Haldane lattice exhibiting the phenomenon of antichiral edge states. The circuit consists of a network of inductors and capacitors with interconnections reproducing the effects of a magnetic vector potential. The next nearest neighbor hoppings are configured differently from the standard Haldane model, and as predicted by earlier theoretical studies, this gives rise to antichiral edge states that propagate in the same direction on opposite edges and coexist with bulk states at the same frequency. Using pickup coils to measure voltage distributions in the circuit, we experimentally verify the key features of the antichiral edge states, including their group velocities and ability to propagate consistently in a Möbius strip configuration.
Similar content being viewed by others
References
F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
M. Z. Hasan, and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010), arXiv: 1002.3895.
X. L. Qi, and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011), arXiv: 1008.2026.
L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photon. 8, 821 (2014), arXiv: 1408.6730.
A. B. Khanikaev, and G. Shvets, Nat. Photon. 11, 763 (2017).
G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Nature 515, 237 (2014), arXiv: 1406.7874.
N. Jia, C. Owens, A. Sommer, D. Schuster, and J. Simon, Phys. Rev. X 5, 021031 (2015).
V. V. Albert, L. I. Glazman, and L. Jiang, Phys. Rev. Lett. 114, 173902 (2015), arXiv: 1410.1243.
T. Hofmann, T. Helbig, C. H. Lee, M. Greiter, and R. Thomale, Phys. Rev. Lett. 122, 247702 (2019).
Z. Q. Zhang, B. L. Wu, J. Song, and H. Jiang, Phys. Rev. B 100, 184202 (2019), arXiv: 1906.04064.
M. Ezawa, Phys. Rev. B 100, 081401 (2019), arXiv: 1904.03823.
S. Raghu, and F. D. M. Haldane, Phys. Rev. A 78, 033834 (2008), arXiv: cond-mat/0602501.
Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, Nature 461, 772 (2009).
Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).
R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).
Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, Phys. Rev. Lett. 114, 114301 (2015), arXiv: 1411.7100.
M. Xiao, W. J. Chen, W. Y. He, and C. T. Chan, Nat. Phys. 11, 920 (2015), arXiv: 1503.06295.
C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005), arXiv: cond-mat/0411737.
B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006), arXiv: cond-mat/0611399.
E. Colomés, and M. Franz, Phys. Rev. Lett. 120, 086603 (2018), arXiv: 1709.01026.
M. Mannaï, and S. Haddad, J. Phys.-Condens. Matter 32, 225501 (2020), arXiv: 1907.11213.
D. Bhowmick, and P. Sengupta, Phys. Rev. B 101, 195133 (2020), arXiv: 1908.04580.
S. Mandal, R. Ge, and T. C. H. Liew, Phys. Rev. B 99, 115423 (2019), arXiv: 1903.07814.
J. Chen, W. Liang, and Z. Y. Li, Phys. Rev. B 101, 214102 (2020).
C. Wang, L. Zhang, P. Zhang, J. Song, and Y. X. Li, Phys. Rev. B 101, 045407 (2020), arXiv: 1904.06649.
M. M. Denner, J. L. Lado, and O. Zilberberg, Phys. Rev. Res. 2, 043190 (2020), arXiv: 2006.13903.
Y. Xu, R. L. Chu, and C. Zhang, Phys. Rev. Lett. 112, 136402 (2014), arXiv: 1310.4100.
C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Commun. Phys. 1, 39 (2018), arXiv: 1705.01077.
T. Goren, K. Plekhanov, F. Appas, and K. L. Hur, Phys. Rev. B 97, 041106 (2018), arXiv: 1711.02034.
K. Luo, J. Feng, Y. X. Zhao, and R. Yu, arXiv: 1810.09231.
K. Luo, R. Yu, and H. Weng, Research 2018, 6793752 (2018).
T. Helbig, T. Hofmann, C. H. Lee, R. Thomale, S. Imhof, L. W. Molenkamp, and T. Kiessling, Phys. Rev. B 99, 161114 (2019), arXiv: 1807.09555.
Y. Hadad, J. C. Soric, A. B. Khanikaev, and A. Alù, Nat. Electron. 1, 178 (2018).
Y. Wang, L. J. Lang, C. H. Lee, B. Zhang, and Y. D. Chong, Nat. Commun. 10, 1102 (2019), arXiv: 1807.11163.
M. Ezawa, Phys. Rev. B 98, 201402 (2018), arXiv: 1809.08847.
S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, F. Schindler, C. H. Lee, M. Greiter, T. Neupert, and R. Thomale, Nat. Phys. 14, 925 (2018), arXiv: 1708.03647.
M. Serra-Garcia, R. Süsstrunk, and S. D. Huber, Phys. Rev. B 99, 020304 (2019).
H. Yang, Z. X. Li, Y. Liu, Y. Cao, and P. Yan, Phys. Rev. Res. 2, 022028 (2020), arXiv: 2004.08274.
R. Yu, Y. X. Zhao, and A. P. Schnyder, Natl. Sci. Rev. 7, 1288 (2020).
Y. Wang, H. M. Price, B. Zhang, and Y. D. Chong, Nat. Commun. 11, 2356 (2020), arXiv: 2001.07427.
Y. Lu, N. Jia, L. Su, C. Owens, G. Juzeliūnas, D. I. Schuster, and J. Simon, Phys. Rev. B 99, 020302 (2019), arXiv: 1807.05243.
W. Zhu, S. Hou, Y. Long, H. Chen, and J. Ren, Phys. Rev. B 97, 075310 (2018), arXiv: 1710.07268.
W. Zhu, Y. Long, H. Chen, and J. Ren, Phys. Rev. B 99, 115410 (2019).
X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, Nat. Mater. 15, 542 (2016).
C. Owens, A. LaChapelle, B. Saxberg, B. M. Anderson, R. Ma, J. Simon, and D. I. Schuster, Phys. Rev. A 97, 013818 (2018), arXiv: 1708.01651.
Author information
Authors and Affiliations
Corresponding authors
Additional information
We thank You Wang, Qiang Wang and Udvas Chattopadhyay from Nanyang Technological University for helpful discussions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874274, and 12004425), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20170058, and BK20200630), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). YiDong Chong was supported by the Singapore MOE Academic Research Fund Tier 3 (Grant No. MOE2016-T3-1-006).
Supplementary Information for
Rights and permissions
About this article
Cite this article
Yang, Y., Zhu, D., Hang, Z. et al. Observation of antichiral edge states in a circuit lattice. Sci. China Phys. Mech. Astron. 64, 257011 (2021). https://doi.org/10.1007/s11433-021-1675-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11433-021-1675-0