Generalization of the theory of three-dimensional quantum Hall effect of Fermi arcs in Weyl semimetal
Mingqi Chang(苌名起)1, Yunfeng Ge(葛云凤)1, and Li Sheng(盛利)1,2,†
1 National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China; 2 Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Abstract The quantum Hall effect (QHE), which is usually observed in two-dimensional systems, was predicted theoretically and observed experimentally in three-dimensional (3D) topological semimetal. However, there are some inconsistencies between the theory and the experiments showing the theory is imperfect. Here, we generalize the theory of the 3D QHE of Fermi arcs in Weyl semimetal. Through calculating the sheet Hall conductivity of a Weyl semimetal slab, we show that the 3D QHE of Fermi arcs can occur in a large energy range and the thickness dependences of the QHE in different Fermi energies are distinct. When the Fermi energy is near the Weyl nodes, the Fermi arcs give rise to the QHE which is independent of the thickness of the slab. When the Fermi energy is not near the Weyl nodes, the two Fermi arcs form a complete Fermi loop with the assistance of bulk states giving rise to the QHE which is dependent on the sample thickness. We also demonstrate how the band anisotropic terms influence the QHE of Fermi arcs. Our theory complements the imperfections of the present theory of 3D QHE of Fermi arcs.
Fund: This work was supported by the National Natural Science Foundation of China (Grant No.11974168)(L.S.).
Corresponding Authors:
Li Sheng,E-mail:shengli@nju.edu.cn
E-mail: shengli@nju.edu.cn
About author: 2022-3-10
Cite this article:
Mingqi Chang(苌名起), Yunfeng Ge(葛云凤), and Li Sheng(盛利) Generalization of the theory of three-dimensional quantum Hall effect of Fermi arcs in Weyl semimetal 2022 Chin. Phys. B 31 057304
[1] Klitzing K V, Dorda G and Pepper M 1980 Phys. Rev. Lett.45 494 [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V and Firsov A A 2005 Nature438 197 [3] Zhang Y, Tan Y W, Stormer H L and Kim P 2005 Nature438 201 [4] Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Nagaosa N, Kawasaki M and Tokura Y 2015 Nat. Commun.6 8530 [5] Thouless D J, Kohmoto M, Nightingale M P and denNijs M 1982 Phys. Rev. Lett.49 405 [6] Halperin B I 1987 Jpn. J. Appl. Phys.26 1913 [7] Kohmoto M, Halperin B I and Wu Y S 1992 Phys. Rev. B45 13488 [8] Koshino M, Aoki H, Kuroki K, Kagoshima S and Osada T 2001 Phys. Rev. Lett.86 1062 [9] Bernevig B A, Hughes T L, Raghu S and Arovas D P 2007 Phys. Rev. Lett.99 146804 [10] Störmer H, Eisenstein J, Gossard A, Wiegmann W and Baldwin K 1986 Phys. Rev. Lett.56 85 [11] Wang P, Ren Y, Tang F, Wang P, Hou T, Zeng H, Zhang L and Qiao Z 2020 Phys. Rev. B101 161201(R) [12] Qin F, Li S, Du Z, Wang C, Zhang W, Yu D, Lu H Z and Xie X C 2020 Phys. Rev. Lett.125 206601 [13] Tang F, Ren Y, Wang P, Zhong R, Schneeloch J, Yang S A, Yang K, Lee P A, Gu G, Qiao Z, et al. 2019 Nature569 537 [14] Chen Rui, Wang C M, Liu Tianyu, Lu H Z and Xie X C 2021 Phys. Rev. Research3 033227 [15] Ma R, Sheng D and Sheng L 2021 Phys. Rev. B104 075425 [16] Wang C M, Sun H P, Lu H Z and Xie X C 2017 Phys. Rev. Lett.119 136806 [17] Lu H Z 2019 National Science Review6 208 [18] Chen Rui, Liu Tianyu, Wang C M, Lu H Z and Xie X C 2021 Phys. Rev. Lett.127 066801 [19] Wan X, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev. B83 205101 [20] Burkov A A and Balents L 2011 Phys. Rev. Lett.107 127205 [21] Yang K Y, Lu Y M and Ran Y 2011 Phys. Rev. B84 075129 [22] Xu G, Weng H, Wang Z, Dai X and Fang Z 2011 Phys. Rev. Lett.107 186806 [23] Delplace P, Li J and Carpentier D 2012 Europhys. Lett.97 67004 [24] Jiang J H 2012 Phys. Rev. A85 033640 [25] Singh B, Sharma A, Lin H, Hasan M, Prasad R and Bansil A 2012 Phys. Rev. B86 115208 [26] Liu J and Vanderbilt D 2014 Phys. Rev. B90 155316 [27] Bulmash D, Liu C X and Qi X L 2014 Phys. Rev. B89 081106(R) [28] Armitage N, Mele E and Vishwanath A 2018 Rev. Mod. Phys.90 015001 [29] Zhang C, Narayan A, Lu S, Zhang J, Zhang H, Ni Z, Yuan X, Liu Y, Park J H, Zhang E, et al. 2017 Nat. Commun.8 1272 [30] Zhang C, Zhang Y, Yuan X, Lu S, Zhang J, Narayan A, Liu Y, Zhang H, Ni Z, Liu R, et al. 2019 Nature565 331 [31] Nishihaya S, Uchida M, Nakazawa Y, Kriener M, Kozuka Y, Taguchi Y and Kawasaki M 2018 Sci. Adv.4 eaar5668 [32] Uchida M, Nakazawa Y, Nishihaya S, Akiba K, Kriener M, Kozuka Y, Miyake A, Taguchi Y, Tokunaga M, Nagaosa N, et al. 2017 Nat. Commun.8 2274 [33] Schumann T, Galletti L, Kealhofer D A, Kim H, Goyal M and Stemmer S 2018 Phys. Rev. Lett.120 016801 [34] Kealhofer D A, Galletti L, Schumann T, Suslov A and Stemmer S 2020 Phys. Rev. X10 011050 [35] Lin B C, Wang S, Wiedmann S, Lu J M, Zheng W Z, Yu D and Liao Z M 2019 Phys. Rev. Lett.122 036602 [36] Zhang S B, Lu H Z and Shen S Q 2016 New J. Phys.18 053039 [37] Shen S Q 2012 Topological Insulators (Berlin Heidelberg: Springer-Verlag) [38] Sun H P and Lu H Z 2019 Frontiers of Physics14 33405 [39] Okugawa R and Murakami S 2014 Phys. Rev. B89 235315 [40] Lu H Z, Zhang S B and Shen S Q 2015 Phys. Rev. B92 045203 [41] Chang M and Sheng L 2021 Phys. Rev. B103 245409
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