Abstract
For a chiral topological semimetal CoSi we experimentally investigate second-harmonic transverse voltage response to ac electrical current for two (normal and in-plane) orientations of magnetic field. Without magnetic field, the observed response depends quadratically on the longitudinal current, as it should be expected for nonlinear Hall effect in topological semimetals. In the external magnetic field, the second-harmonic Hall voltage shows odd-type dependence on the field direction for both field orientations. In normal field, this sensitivity to the field direction allows to exclude possible contribution of the thermopower effects, so the second-harmonic transverse voltage response indeed originates from the nonlinear Hall effect. In contrast, for the in-plane fields, odd-type field dependence is a clear demonstration of a novel planar nonlinear Hall effect for chiral CoSi semimetal.
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REFERENCES
N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).
P. K. Das, D. D. Sante, I. Vobornik, J. Fujii, T. Okuda, E. Bruyer, A. Gyenis, B. E. Feldman, J. Tao, R. Ciancio, G. Rossi, M. N. Ali, S. Picozzi, A. Yadzani, G. Panaccione, and R. J. Cava, Nat. Commun. 7, 10847 (2016).
B. Feng, Y.-H. Chan, Y. Feng, R.-Y. Liu, M.-Y. Chou, K. Kuroda, K. Yaji, A. Harasawa, P. Moras, A. Barinov, W. Malaeb, C. Bareille, T. Kondo, S. Shin, F. Komori, T.-C. Chiang, Y. Shi, and I. Matsuda, Phys. Rev. B 94, 195134 (2016).
B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science (Washington, DC, U. S.) 353, aaf5037 (2016).
P. Tang, Q. Zhou, and Sh.-Ch. Zhang, Phys. Rev. Lett. 119, 206402 (2017).
N. B. Schröter, D. Pei, M. G. Vergniory, Y. Sun, K. Manna, F. de Juan, J. A. Krieger, V. Süss, M. Schmidt, P. Dudin, B. Bradlyn, T. K. Kim, Th. Schmitt, C. Cacho, C. Felser, V. N. Strocov and Y. Chen, Nat. Phys. 15, 759 (2019).
Zh. Rao, H. Li, T. Zhang, Sh. Tian, Ch. Li, B. Fu, C. Tang, L. Wang, Zh. Li, W. Fan, J. Li, Y. Huang, Zh. Liu, Y. Long, Ch. Fang, H. Weng, Y. Shi, H. Lei, Y. Sun, T. Qian, and H. Ding, Nature (London, U.K.) 567, 496 (2019).
D. Takane, Zh. Wang, S. Souma, K. Nakayama, T. Nakamura, H. Oinuma, Y. Nakata, H. Iwasawa, C. Cacho, T. Kim, K. Horiba, H. Kumigashira, T. Takahashi, Y. Ando, and T. Sato, Phys. Rev. Lett. 122, 076402 (2019).
N. B. M. Schröter, S. Stolz, K. Manna, F. Juan, M. G. Vergniory, J. A. Krieger, D. Pei, Th. Schmitt, P. Dudin, T. K. Kim, C. Cacho, B. Bradlyn, H. Borrmann, M. Schmidt, R. Widmer, et al., Science (Washington, DC, U. S.) 369, 179 (2020).
I. Sodemann and L. Fu, Phys. Rev. Lett. 115, 216806 (2015).
T. Low, Y. Jiang, and F. Guinea, Phys. Rev. B 92, 235447 (2015).
Y. Zhang, J. van den Brink, C. Felser, and B. Yan, 2D Mater. 5, 044001 (2018).
Z. Z. Du, C. M. Wang, H.-Z. Lu, and X. C. Xie, Phys. Rev. Lett. 121, 266601 (2018).
Z. Z. Du, C. M. Wang, S. Li, H.-Z. Lu, and X. C. Xie, Nat. Commun. 10, 3047 (2019).
C. Xiao, Z. Z. Du, and Q. Niu, Phys. Rev. B 100, 165422 (2019).
S. Nandy and I. Sodemann, Phys. Rev. B 100, 195117 (2019).
H. Wang and X. Qian, npj Comput. Mater. 5, 1 (2019).
B. T. Zhou, C.-P. Zhang, and K. T. Law, Phys. Rev. Appl. 13, 024053 (2020).
H. Rostami and V. Jurićić, Phys. Rev. Res. 2, 013069 (2020).
D.-F. Shao, S.-H. Zhang, G. Gurung, W. Yang, and E. Y. Tsymbal, Phys. Rev. Lett. 124, 067203 (2020).
S. Singh, J. Kim, K. M. Rabe, and D. Vanderbilt, Phys. Rev. Lett. 125, 046402 (2020). https://doi.org/10.1103/Phys-RevLett.125.046402
M. W.-Y. Tu, C. Li, H. Yu, and W. Yao, 2D Mater. (2020). https://doi.org/10.1088/2053-1583/ab89e8
Z. Z. Du, C. M. Wang, Hai-Peng Sun, Hai-Zhou Lu, and X. C. Xie, arXiv: 2004.09742 (2020).
Q. Ma, S.-Y. Xu, H. Shen, D. MacNeill, V. Fatemi, T.‑R. Chang, et al., Nature (London, U.K.) 565, 337 (2019).
K. Kang, T. Li, E. Sohn, J. Shan, and K. F. Mak, Nat. Mater. 18, 324 (2019).
O. O. Shvetsov, V. D. Esin, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, JETP Lett. 109, 715 (2019). https://doi.org/10.1134/S0021364019110018
A. Tiwari, F. Chen, Sh. Zhong, E. Drueke, J. Koo, A. Kaczmarek, C. Xiao, J. Gao, X. Luo, Q. Niu, Y. Sun, B. Yan, L. Zhao, and A. W. Tsen, Nat. Commun. 12, 2049 (2021). https://doi.org/10.1038/s41467-021-22343-5
P. He, S. S.-L. Zhang, D. Zhu, Sh. Shi, O. G. Heinonen, G. Vignale, and H. Yang, Phys. Rev. Lett. 123, 016801 (2019).
N. Kumar, S. N. Guin, C. Felser, and C. Shekhar, Phys. Rev. B 98, 041103 (2018).
F. C. Chen, X. Luo, J. Yan, Y. Sun, H. Y. Lv, W. J. Lu, C. Y. Xi, P. Tong, Z. G. Sheng, X. B. Zhu, W. H. Song, and Y. P. Sun, Phys. Rev. B 98, 041114 (2018).
D. D. Liang, Y. J. Wang, W. L. Zhen, J. Yang, S. R. Weng, X. Yan, Y. Y. Han, W. Tong, W. K. Zhu, L. Pi, and C. J. Zhang, AIP Adv. 9, 055015 (2019).
P. Li, C. Zhang, Y. Wen, L. Cheng, G. Nichols, D. G. Cory, G.-X. Miao, and X.-X. Zhang, Phys. Rev. B 100, 205128 (2019).
A. A. Burkov, Phys. Rev. B 96, 041110 (2017).
S. Nandy, G. Sharma, A. Taraphder, and S. Tewari, Phys. Rev. Lett. 119, 176804 (2017).
D. Ma, H. Jiang, H. Liu, and X. C. Xie, Phys. Rev. B 99, 115121 (2019).
O. O. Shvetsov, V. D. Esin, Yu. S. Barash, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Phys. Rev. B 101, 035304 (2020). https://doi.org/10.1103/PhysRevB.101.035304
O. O. Shvetsov, V. D. Esin, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Phys. Rev. B 99, 125305 (2019). https://doi.org/10.1103/PhysRevB.99.125305
D. S. Wu, Z. Y. Mi, Y. J. Li, W. Wu, P. L. Li, Y. T. Song, G. T. Liu, G. Li, and J. L. Luo, Chin. Phys. Lett. 36, 077102 (2019).
O. O. Shvetsov, A. Kononov, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, JETP Lett. 107, 774 (2018). https://doi.org/10.1134/S0021364018120020
O. O. Shvetsov, A. Kononov, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Eur. Phys. Lett. 124, 47003 (2018). https://doi.org/10.1209/0295-5075/124/47003
A. Kononov, O. O. Shvetsov, S. V. Egorov, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Eur. Phys. Lett. 122, 27004 (2018). https://doi.org/10.1209/0295-5075/122/27004
C. Fu, Th. Scaffidi, J. Waissman, Y. Sun, R. Saha, S. J. Watzman, A. K. Srivastava, G. Li, W. Schnelle, P. Werner, M. E. Kamminga, S. Sachdev, S. S. P. Parkin, S. A. Hartnoll, C. Felser, and J. Gooth, arXiv: 1802.09468.
T. Zhou, Ch. Zhang, H. Zhang, F. Xiu, and Zh. Yang, Inorg. Chem. Front. 3, 1637 (2016).
R. Lundgren, P. Laurell, and G. A. Fiete, Phys. Rev. B 90, 165115 (2014). https://doi.org/10.1103/Phys-RevB.90.165115
K. Das and A. Agarwal, Phys. Rev. B 100, 085406 (2019). https://doi.org/10.1103/PhysRevB.100.085406
N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010).
H. Isobe, S.-Y. Xu, and L. Fu, Sci. Adv. 6, eaay2497 (2020). https://doi.org/10.1126/sciadv.aay2497
A. A. Zyuzin and A. Yu. Zyuzin, Phys. Rev. B 95, 085127 (2017). https://doi.org/10.1103/PhysRevB.95.085127
R.-H. Li, O. G. Heinonen, A. A. Burkov, and S. S.‑L. Zhang, Phys. Rev. B 103, 045105 (2021).
ACKNOWLEDGMENTS
We wish to thank V.T. Dolgopolov for fruitful discussions, and S.S Khasanov for X-ray sample characterization. We gratefully acknowledge financial support by the RF State task.
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Esin, V.D., Timonina, A.V., Kolesnikov, N.N. et al. Nonlinear Planar Hall Effect in Chiral Topological Semimetal CoSi. J. Exp. Theor. Phys. 133, 792–797 (2021). https://doi.org/10.1134/S1063776121120037
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DOI: https://doi.org/10.1134/S1063776121120037