| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Strain Tunable Berry Curvature Dipole, Orbital Magnetization and Nonlinear Hall Effect in WSe$_{2}$ Monolayer |
| Mao-Sen Qin , Peng-Fei Zhu , Xing-Guo Ye , Wen-Zheng Xu , Zhen-Hao Song , Jing Liang , Kaihui Liu , and Zhi-Min Liao* |
| State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China |
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| Cite this article: |
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Mao-Sen Qin , Peng-Fei Zhu , Xing-Guo Ye et al 2021 Chin. Phys. Lett. 38 017301 |
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Abstract The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent $K$ and $K'$ valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe$_2$ via applying uniaxial strain to break $C_{3v}$ symmetry. As a result, although the Berry curvature itself is still opposite in $K$ and $K'$ valleys, the two valleys would contribute equally to nonzero Berry curvature dipole. Upon applying electric field ${\boldsymbol E}$, the emergent Berry curvature dipole ${\boldsymbol D}$ would lead to an out-of-plane orbital magnetization $M \propto {\boldsymbol D} \cdot {\boldsymbol E}$, which further induces an anomalous Hall effect with a linear response to $E^2$, known as nonlinear Hall effect. We show the strain modulated transport properties of nonlinear Hall effect in monolayer WSe$_2$ with moderate hole-doping by gating. The second-harmonic Hall signals show quadratic dependence on electric field, and the corresponding orbital magnetization per current density $M/J$ can reach as large as 60. In contrast to the conventional Rashba–Edelstein effect with in-plane spin polarization, such current-induced orbital magnetization is along the out-of-plane direction, thus promising for high-efficient electrical switching of perpendicular magnetization.
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Received: 12 November 2020
Published: 03 December 2020
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| Fund: Supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0703703 and 2016YFA0300802), and the National Natural Science Foundation of China (Grant Nos. 91964201, 61825401, and 11774004). |
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| [1] | Xiao D, Chang M C and Niu Q 2010 Rev. Mod. Phys. 82 1959 |
| [2] | Chang M C and Niu Q 1995 Phys. Rev. Lett. 75 1348 |
| [3] | Chang M C and Niu Q 1996 Phys. Rev. B 53 7010 |
| [4] | Nagaosa N, Sinova J, Onoda S, MacDonald A H and Ong N P 2010 Rev. Mod. Phys. 82 1539 |
| [5] | Xiao D, Yao W and Niu Q 2007 Phys. Rev. Lett. 99 236809 |
| [6] | Dau M T, Vergnaud C, Marty A, Beigné C, Gambarelli S, Maurel V, Journot T, Hyot B, Guillet T, Grévin B, Okuno H and Jamet M 2019 Nat. Commun. 10 5796 |
| [7] | Dai X, Du Z Z and Lu H Z 2017 Phys. Rev. Lett. 119 166601 |
| [8] | Xiao D, Shi J and Niu Q 2005 Phys. Rev. Lett. 95 137204 |
| [9] | Sodemann I and Fu L 2015 Phys. Rev. Lett. 115 216806 |
| [10] | Deyo E, Golub L E, Ivchenko E L and Spivak B 2009 arXiv:0904.1917 [cond-mat.mes-hall] |
| [11] | You J S, Fang S, Xu S Y, Kaxiras E and Low T 2018 Phys. Rev. B 98 121109 |
| [12] | Du Z Z, Wang C M, Li S, Lu H Z and Xie X C 2019 Nat. Commun. 10 3047 |
| [13] | Zhang Y, van den Brink J, Felser C and Yan B 2018 2D Mater. 5 044001 |
| [14] | Xiao C, Du Z Z and Niu Q 2019 Phys. Rev. B 100 165422 |
| [15] | Yu X Q, Zhu Z G, You J S, Low T and Su G 2019 Phys. Rev. B 99 201410 |
| [16] | Du Z Z, Wang C M, Sun H P, Lu H Z and Xie X C 2020 arXiv:2004.09742 [cond-mat.mes-hall] |
| [17] | Xu S Y, Ma Q, Shen H, Fatemi V, Wu S, Chang T R, Chang G, Valdivia A M M, Chan C K, Gibson Q D, Zhou J, Liu Z, Watanabe K, Taniguchi T, Lin H, Cava R J, Fu L, Gedik N and Jarillo-Herrero P 2018 Nat. Phys. 14 900 |
| [18] | Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Mier V A M, Wu S, Du Z, Hsu C H, Fang S, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Kaxiras E, Lu H Z, Lin H, Fu L, Gedik N and Jarillo-Herrero P 2019 Nature 565 337 |
| [19] | Kang K, Li T, Sohn E, Shan J and Mak K F 2019 Nat. Mater. 18 324 |
| [20] | Wang H and Qian X F 2019 npj Comput. Mater. 5 119 |
| [21] | Xiao J, Wang Y, Wang H, Pemmaraju C D, Wang S, Muscher P, Sie E J, Nyby C M, Devereaux T P, Qian X, Zhang X and Lindenberg A M 2020 Nat. Phys. 16 1028 |
| [22] | Yao W, Xiao D and Niu Q 2008 Phys. Rev. B 77 235406 |
| [23] | Xu X, Yao W, Xiao D and Heinz T F 2014 Nat. Phys. 10 343 |
| [24] | Zeng H, Dai J, Yao W, Xiao D and Cui X 2012 Nat. Nanotechnol. 7 490 |
| [25] | Mak K F, He K, Shan J and Heinz T F 2012 Nat. Nanotechnol. 7 494 |
| [26] | Wu S, Ross J S, Liu G B, Aivazian G, Jones A, Fei Z, Zhu W, Xiao D, Yao W, Cobden D and Xu X 2013 Nat. Phys. 9 149 |
| [27] | Xiao D, Liu G B, Feng W, Xu X and Yao W 2012 Phys. Rev. Lett. 108 196802 |
| [28] | Conley H J, Wang B, Ziegler J I, Haglund R F, Pantelides S T and Bolotin K I 2013 Nano Lett. 13 3626 |
| [29] | Lee J, Wang Z, Xie H, Mak K F and Shan J 2017 Nat. Mater. 16 887 |
| [30] | Son J, Kim K H, Ahn Y H, Lee H W and Lee J 2019 Phys. Rev. Lett. 123 036806 |
| [31] | Peng J, Luo H, Lin D, Xu H, He T and Jin W 2004 Appl. Phys. Lett. 85 6221 |
| [32] | Cai K, Yang M, Ju H, Wang S, Ji Y, Li B, Edmonds K W, Sheng Y, Zhang B, Zhang N, Liu S, Zheng H and Wang K 2017 Nat. Mater. 16 712 |
| [33] | Li F, Zhang S, Yang T, Xu Z, Zhang N, Liu G, Wang J, Wang J, Cheng Z, Ye Z G, Luo J, Shrout T R and Chen L Q 2016 Nat. Commun. 7 13807 |
| [34] | Hou W, Azizimanesh A, Sewaket A, Peña T, Watson C, Liu M, Askari H and Wu S M 2019 Nat. Nanotechnol. 14 668 |
| [35] | Ye J T, Zhang Y J, Akashi R, Bahramy M S, Arita R and Iwasa Y 2012 Science 338 1193 |
| [36] | Zhang Q, Cheng Y, Gan L Y and Schwingenschlögl U 2013 Phys. Rev. B 88 245447 |
| [37] | Shi H, Pan H, Zhang Y W and Yakobson B I 2013 Phys. Rev. B 87 155304 |
| [38] | Rostami H, Roldán R, Cappelluti E, Asgari R and Guinea F 2015 Phys. Rev. B 92 195402 |
| [39] | Peelaers H and Van de Walle C G 2012 Phys. Rev. B 86 241401 |
| [40] | Chen Y, Zhang Y, Keil R, Zopf M, Ding F and Schmidt O G 2017 Nano Lett. 17 7864 |
| [41] | Tsai M Y, Tarasov A, Hesabi Z R, Taghinejad H, Campbell P M, Joiner C A, Adibi A and Vogel E M 2015 ACS Appl. Mater. & Interfaces 7 12850 |
| [42] | Kormányos A, Burkard G, Gmitra M, Fabian J, Zólyomi V, Drummond N D and Fal'ko V 2015 2D Mater. 2 022001 |
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