Berry curvature-induced emerging magnetic response in two-dimensional materials

Liu Yu-Ting; He Wen-Yu; Liu Jun-Wei; Shao Qi-Ming

doi:10.7498/aps.70.20202132

Abstract

The magnetic response in a two-dimensional material has received increasing attention in recent years. The magnetic effects and related quantum transport originate from Berry curvature, which is associated with crystal symmetry and many quantum effects including electrons’ orbital magnetism, spin-orbit coupling, and magnetoelectricity. The importance of studying the magnetic response in the two-dimensional material lies in two aspects. First, the magnetic response of two-dimensional material provides a platform to investigate the coupling between the above-mentioned intrinsic quantum effects and their couplings. Second, it possesses the potential applications in energy-efficient quantum and spintronic devices. Here, we review the experimental research progress made in recent years. In particular, we focus on the research progress of the valley Hall and magnetoelectric effect, quantum non-linear Hall effect, anomalous Hall, and quantum anomalous Hall effect in two-dimensional materials such as graphene, transition-metal chalcogenides, and twisted bilayer graphene. For each session, we first introduce these phenomena and their underlying physics by using crystal symmetries and band structures. Then, we summarize the experimental results and identify unsolved problems. At last, we provide an outlook in this emerging research direction.

Keywords:

Authors and contacts

1.
Department of Electronic and Computing Engineering, The Hong Kong University of Science and Technology, Hong Kong 999077, China
2.
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong 999077, China

Corresponding author: Shao Qi-Ming, eeqshao@ust.hk

Funds: Project supported by the HK University Grant Committee (Grant Nos. ECS26200520, N_HKUST626/18, 26302118, 16305019), the HKUST ECE Start-up Fund, and the HKUST Postdoctoral Fellowship Matching Fund (Grant No. NA389)

FullText HTML : translate this paragraph

References

[1]	Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A, Goldhaber-Gordon D 2019 Science 365 605 Google Scholar
[2]	Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L, Young A F 2020 Science 367 900 Google Scholar
[3]	Zhang Y H, Mao D, Senthil T 2019 Phys. Rev. Res. 1 033126 Google Scholar
[4]	Sjöstrand T J, Karlsson K, Aryasetiawan F 2019 Phys. Rev. B 100 054427 Google Scholar
[5]	Xiao D, Yao Y, Fang Z, Niu Q 2006 Phys. Rev. Lett. 97 026603 Google Scholar
[6]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[7]	Murakami S 2006 Phys. Rev. Lett. 97 236805 Google Scholar
[8]	Essin A M, Turner A M, Moore J E, Vanderbilt D 2010 Phys. Rev. B 81 205104 Google Scholar
[9]	Essin A M, Moore J E, Vanderbilt D 2009 Phys. Rev. Lett. 102 146805 Google Scholar
[10]	Malashevich A, Souza I, Coh S, Vanderbilt D 2010 New J. Phys. 12 053032 Google Scholar
[11]	Xiao D, Shi J, Niu Q 2005 Phys. Rev. Lett. 95 137204 Google Scholar
[12]	Thonhauser T, Ceresoli D, Vanderbilt D, Resta R 2005 Phys. Rev. Lett. 95 137205 Google Scholar
[13]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google Scholar
[14]	Schaibley J R, Yu H, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 1
[15]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[16]	Saito R, Tatsumi Y, Huang S, Ling X, Dresselhaus M S 2016 J. Phys. Condens. Matter 28 353002 Google Scholar
[17]	Zhao S, Dong B, Wang H, Wang H, Zhang Y, Han Z V, Zhang H 2020 Nanoscale Adv. 2 109 Google Scholar
[18]	Qian X, Liu J, Fu L, Li J 2014 Science 346 1344 Google Scholar
[19]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[20]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[21]	Li L, Yang F, Ye G J, Zhang Z, Zhu Z, Lou W, Zhou X, Li L, Watanabe K, Taniguchi T, Chang K, Wang Y, Chen X H, Zhang Y 2016 Nat. Nanotechnol. 11 593 Google Scholar
[22]	Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76 Google Scholar
[23]	Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002 Google Scholar
[24]	Kim J, Jin C, Chen B, Cai H, Zhao T, Lee P, Kahn S, Watanabe K, Taniguchi T, Tongay S, Crommie M F, Wang F 2017 Sci. Adv. 3 e1700518 Google Scholar
[25]	Lee J, Wang Z, Xie H, Mak K F, Shan J 2017 Nat. Mater. 16 887 Google Scholar
[26]	Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M 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, Jarillo-Herrero P 2019 Nature 565 337 Google Scholar
[27]	Kang K, Li T, Sohn E, Shan J, Mak K F 2019 Nat. Mater. 18 324 Google Scholar
[28]	Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213
[29]	Fiebig M 2005 J. Phys. Appl. Phys. 38 R123 Google Scholar
[30]	Rycerz A, Tworzydło J, Beenakker C W J 2007 Nat. Phys. 3 172 Google Scholar
[31]	Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489 Google Scholar
[32]	Gorbachev R V, Song J C W, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448 Google Scholar
[33]	Sui M, Chen G, Ma L, Shan W Y, Tian D, Watanabe K, Taniguchi T, Jin X, Yao W, Xiao D, Zhang Y 2015 Nat. Phys. 11 1027 Google Scholar
[34]	Shimazaki Y, Yamamoto M, Borzenets I V, Watanabe K, Taniguchi T, Tarucha S 2015 Nat. Phys. 11 1032 Google Scholar
[35]	Lee J, Mak K F, Shan J 2016 Nat. Nanotechnol. 11 421 Google Scholar
[36]	Huang Z, Liu Y, Dini K, Tan Q, Liu Z, Fang H, Liu J, Liew T, Gao W 2020 Nano Lett. 20 1345 Google Scholar
[37]	Zhang Y J, Oka T, Suzuki R, Ye J T, Iwasa Y 2014 Science 344 725 Google Scholar
[38]	Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290 Google Scholar
[39]	Kim J, Hong X, Jin C, Shi S F, Chang C Y S, Chiu M H, Li L J, Wang F 2014 Science 346 1205 Google Scholar
[40]	Li Y, Ludwig J, Low T, Chernikov A, Cui X, Arefe G, Kim Y D, van der Zande A M, Rigosi A, Hill H M, Kim S H, Hone J, Li Z, Smirnov D, Heinz T F 2014 Phys. Rev. Lett. 113 266804 Google Scholar
[41]	Srivastava A, Sidler M, Allain A V, Lembke D S, Kis A, Imamoğlu A 2015 Nat. Phys. 11 141 Google Scholar
[42]	Aivazian G, Gong Z, Jones A M, Chu R L, Yan J, Mandrus D G, Zhang C, Cobden D, Yao W, Xu X 2015 Nat. Phys. 11 148 Google Scholar
[43]	Xu X, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343 Google Scholar
[44]	MacNeill D, Heikes C, Mak K F, Anderson Z, Kormányos A, Zólyomi V, Park J, Ralph D C 2015 Phys. Rev. Lett. 114 037401 Google Scholar
[45]	Ye Y, Xiao J, Wang H, Ye Z, Zhu H, Zhao M, Wang Y, Zhao J, Yin X, Zhang X 2016 Nat. Nanotechnol. 11 598 Google Scholar
[46]	Cracknell A P1975 Magnetism in Crystalline Materials (1st Ed.) (Oxford: Pergamon Press)
[47]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[48]	Zeng H, Dai J, Yao W, Xiao D, Cui X 2012 Nat. Nanotechnol. 7 490 Google Scholar
[49]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[50]	Weng H, Yu R, Hu X, Dai X, Fang Z 2015 Adv. Phys. 64 227 Google Scholar
[51]	de Juan F, Grushin A G, Morimoto T, Moore J E 2017 Nat. Commun. 8 15995 Google Scholar
[52]	You J S, Fang S, Xu S Y, Kaxiras E, Low T 2018 Phys. Rev. B 98 121109R Google Scholar
[53]	Zhang Y, Brink J van den, Felser C, Yan B 2018 2D Mater. 5 044001
[54]	Shi L, Song J C W 2019 Phys. Rev. B 99 035403 Google Scholar
[55]	Tian Y, Li Y, Jin X 2009 Phys. Rev. Lett. 103 087206 Google Scholar
[56]	Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, Deviatov E V 2019 JETP Lett. 109 715 Google Scholar
[57]	Huang M, Wu Z, Hu J, Cai X, Li E, An L, Feng X, Ye Z, Lin N, Law K T, Wang N 2020 arXiv: 2006.05615 [cond-mat.mes-hall]
[58]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji ZQ, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[59]	刘健鹏, 戴希 2020 69 147301 Google Scholar Liu J P, Dai X 2020 Acta Phys. Sin. 69 147301 Google Scholar
[60]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[61]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C and Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[62]	Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F 2020 Nature 579 56 Google Scholar
[63]	Chen S, He M, Zhang Y H, Hsieh V, Fei Z, Watanabe K, Taniguchi T, Cobden D H, Xu X, Dean C R, Yankowitz M 2020 Nat. Phys. 17 374
[64]	Polshyn H, Zhu J, Kumar M A, Zhang Y, Yang F, Tschirhart C L, Serlin M, Watanabe K, Taniguchi T, MacDonald A H, Young A F 2020 Nature 588 66 Google Scholar
[65]	Zhu J, Su J J, MacDonald A H 2020 Phys. Rev. Lett. 125 227702 Google Scholar
[66]	Cao Y, Luo J Y, Fatemi V, Fang S, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2016 Phys. Rev. Lett. 117 116804 Google Scholar
[67]	Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F, Dean C R 2019 Science 363 1059 Google Scholar
[68]	Kerelsky A, McGilly L J, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A, Pasupathy A N 2019 Nature 572 95 Google Scholar
[69]	Choi Y, Kemmer J, Peng Y, Thomson A, Arora H, Polski R, Zhang Y, Ren H, Alicea J, Refael G, von Oppen F, Watanabe K, Taniguchi T, Nadj-Perge S 2019 Nat. Phys. 15 1174 Google Scholar
[70]	Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237 Google Scholar
[71]	Lee D S, Riedl C, Beringer T, Castro Neto A H, von Klitzing K, Starke U, Smet J H 2011 Phys. Rev. Lett. 107 216602 Google Scholar
[72]	Kim Y, Park J, Song I, Ok J M, Jo Y, Watanabe K, Taniquchi T, Choi H C, Lee D S, Jung S, Kim J S 2016 Sci. Rep. 6 38068 Google Scholar
[73]	Moon P, Koshino M 2012 Phys. Rev. B 85 195458 Google Scholar
[74]	He W Y, Goldhaber-Gordon D, Law K T 2020 Nat. Commun. 11 1650 Google Scholar
[75]	He W Y, Law K T 2020 Phys. Rev. Res. 2 012073 Google Scholar
[76]	Liu Y, Shao Q 2020 ACS Nano 14 9389 Google Scholar
[77]	Xie M, MacDonald A H 2020 Phys. Rev. Lett. 124 097601 Google Scholar
[78]	Bultinck N, Chatterjee S, Zaletel M P 2020 Phys. Rev. Lett. 124 166601 Google Scholar
[79]	Peng R, Ma Y, Xu X, He Z, Huang B, Dai Y 2020 Phys. Rev. B 102 035412 Google Scholar
[80]	Ma Y, Kou L, Du A, Huang B, Dai Y, Heine T 2018 Phys. Rev. B 97 035444 Google Scholar
[81]	Xu Z, Zhang Q, Shen Q, Cheng Y, Schwingenschlögl U, Huang W 2017 J. Mater. Chem. C 5 10427 Google Scholar
[82]	Fu L 2009 Phys. Rev. Lett. 103 266801 Google Scholar
[83]	Alpichshev Z, Analytis J G, Chu J H, Fisher I R, Chen Y L, Shen Z X, Fang A, Kapitulnik A 2010 Phys. Rev. Lett. 104 016401 Google Scholar
[84]	Hosur P 2011 Phys. Rev. B 83 035309 Google Scholar
[85]	Zheng Z, Ma Q, Bi Z, de la Barrera S, Liu M H, Mao N, Zhang Y, Kiper N, Watanabe K, Taniguchi T, Kong J, Tisdale W A, Ashoori R, Gedik N, Fu L, Xu S Y, Jarillo-Herrero P 2020 Nature 588 71 Google Scholar

Cited By

图 1 受应力的单层硫化钼谷磁电效应示意图　(a)谷霍尔效应^[22]; (b)谷磁电效应^[25]; (c)自旋极化引起的磁矩和谷磁电性引起的磁矩在外磁场下的磁光克尔响应; (d)磁光克尔响应与施加电流方向和应力方向的关系

Figure 1. Sketch of the magnetoelectric effect in monolayer MoS₂: (a) Valley Hall effect^[22]; (b) valley magnetoelectricity^[25]; (c) comparison of magneto-optical Kerr response between spin polarizations induced magnetism and valley magnetization under external magnetic fields; (d) valley magnetization-induced Kerr rotation as a function of the azimuthal angle of current for zigzag and armchair monolayer MoS₂.

DownLoad: Full-Size Img PowerPoint

图 2 碲化钨中量子非线性霍尔效应示意图　(a)线性和非线性霍尔电压随电流的变化^[47]; (b)碲化钨在不同方向上的晶体结构示意图; (c)纵向电压和非线性霍尔电压与电流施加方向的关系^[27]; (d)非线性霍尔电压与材料电导率的关系. 插图表示了非线性霍尔效应的两种来源: 贝里曲率和电子偏散射输运^[27]

Figure 2. Illustration of the quantum nonlinear Hall effect: (a) Dependence of linear and non-linear Hall voltage on applied currents^[47]; (b) crystal structure of WTe₂; (c) angular dependence of longitudinal voltage and non-linear Hall voltage^[27]; (d) relationship between nonlinear Hall voltage and conductance. The inset shows two origins of nonlinear Hall voltage: Intrinsic Berry curvature and skew scattering^[27].

DownLoad: Full-Size Img PowerPoint

图 3 转角双层石墨烯中量子反常霍尔效应示意图　(a)自旋磁化和轨道磁化中量子反常霍尔效应对比示意图; (b)转角双层石墨烯中自旋极化和能谷非极化的导带示意图; (c)转角双层石墨烯中自旋和能谷完全极化的导带示意图; (d)量子反常霍尔态下, 霍尔电阻和纵向电阻随磁场的变化关系, 插图表示材料的导电状态—边缘导电和体导电; (e)电流控制反常霍尔态下磁性翻转示意图

Figure 3. Illustration of quantum anomalous Hall effect in twisted bilayer graphene (tBLG): (a) Sketch of quantum anomalous Hall effect in spin magnetization and orbital magnetization systems; (b) schematic of fully spin-polarized and but valley-unpolarized conduction bands in a moiré unit cell of tBLG; (c) schematic of fully spin-polarized and valley-polarized conduction bands in a moiré unit cell of tBLG; (d) longitudinal resistance and Hall resistance as a function of magnetic field in the quantum anomalous Hall state, and the insets show the bulk and edge conduction states of material; (e) current control of magnetization switching in the anomalous Hall state.

DownLoad: Full-Size Img PowerPoint

map

[1]	Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A, Goldhaber-Gordon D 2019 Science 365 605 Google Scholar
[2]	Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L, Young A F 2020 Science 367 900 Google Scholar
[3]	Zhang Y H, Mao D, Senthil T 2019 Phys. Rev. Res. 1 033126 Google Scholar
[4]	Sjöstrand T J, Karlsson K, Aryasetiawan F 2019 Phys. Rev. B 100 054427 Google Scholar
[5]	Xiao D, Yao Y, Fang Z, Niu Q 2006 Phys. Rev. Lett. 97 026603 Google Scholar
[6]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[7]	Murakami S 2006 Phys. Rev. Lett. 97 236805 Google Scholar
[8]	Essin A M, Turner A M, Moore J E, Vanderbilt D 2010 Phys. Rev. B 81 205104 Google Scholar
[9]	Essin A M, Moore J E, Vanderbilt D 2009 Phys. Rev. Lett. 102 146805 Google Scholar
[10]	Malashevich A, Souza I, Coh S, Vanderbilt D 2010 New J. Phys. 12 053032 Google Scholar
[11]	Xiao D, Shi J, Niu Q 2005 Phys. Rev. Lett. 95 137204 Google Scholar
[12]	Thonhauser T, Ceresoli D, Vanderbilt D, Resta R 2005 Phys. Rev. Lett. 95 137205 Google Scholar
[13]	Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959 Google Scholar
[14]	Schaibley J R, Yu H, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 1
[15]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[16]	Saito R, Tatsumi Y, Huang S, Ling X, Dresselhaus M S 2016 J. Phys. Condens. Matter 28 353002 Google Scholar
[17]	Zhao S, Dong B, Wang H, Wang H, Zhang Y, Han Z V, Zhang H 2020 Nanoscale Adv. 2 109 Google Scholar
[18]	Qian X, Liu J, Fu L, Li J 2014 Science 346 1344 Google Scholar
[19]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[20]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[21]	Li L, Yang F, Ye G J, Zhang Z, Zhu Z, Lou W, Zhou X, Li L, Watanabe K, Taniguchi T, Chang K, Wang Y, Chen X H, Zhang Y 2016 Nat. Nanotechnol. 11 593 Google Scholar
[22]	Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76 Google Scholar
[23]	Weng H, Dai X, Fang Z 2014 Phys. Rev. X 4 011002 Google Scholar
[24]	Kim J, Jin C, Chen B, Cai H, Zhao T, Lee P, Kahn S, Watanabe K, Taniguchi T, Tongay S, Crommie M F, Wang F 2017 Sci. Adv. 3 e1700518 Google Scholar
[25]	Lee J, Wang Z, Xie H, Mak K F, Shan J 2017 Nat. Mater. 16 887 Google Scholar
[26]	Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M 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, Jarillo-Herrero P 2019 Nature 565 337 Google Scholar
[27]	Kang K, Li T, Sohn E, Shan J, Mak K F 2019 Nat. Mater. 18 324 Google Scholar
[28]	Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213
[29]	Fiebig M 2005 J. Phys. Appl. Phys. 38 R123 Google Scholar
[30]	Rycerz A, Tworzydło J, Beenakker C W J 2007 Nat. Phys. 3 172 Google Scholar
[31]	Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489 Google Scholar
[32]	Gorbachev R V, Song J C W, Yu G L, Kretinin A V, Withers F, Cao Y, Mishchenko A, Grigorieva I V, Novoselov K S, Levitov L S, Geim A K 2014 Science 346 448 Google Scholar
[33]	Sui M, Chen G, Ma L, Shan W Y, Tian D, Watanabe K, Taniguchi T, Jin X, Yao W, Xiao D, Zhang Y 2015 Nat. Phys. 11 1027 Google Scholar
[34]	Shimazaki Y, Yamamoto M, Borzenets I V, Watanabe K, Taniguchi T, Tarucha S 2015 Nat. Phys. 11 1032 Google Scholar
[35]	Lee J, Mak K F, Shan J 2016 Nat. Nanotechnol. 11 421 Google Scholar
[36]	Huang Z, Liu Y, Dini K, Tan Q, Liu Z, Fang H, Liu J, Liew T, Gao W 2020 Nano Lett. 20 1345 Google Scholar
[37]	Zhang Y J, Oka T, Suzuki R, Ye J T, Iwasa Y 2014 Science 344 725 Google Scholar
[38]	Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290 Google Scholar
[39]	Kim J, Hong X, Jin C, Shi S F, Chang C Y S, Chiu M H, Li L J, Wang F 2014 Science 346 1205 Google Scholar
[40]	Li Y, Ludwig J, Low T, Chernikov A, Cui X, Arefe G, Kim Y D, van der Zande A M, Rigosi A, Hill H M, Kim S H, Hone J, Li Z, Smirnov D, Heinz T F 2014 Phys. Rev. Lett. 113 266804 Google Scholar
[41]	Srivastava A, Sidler M, Allain A V, Lembke D S, Kis A, Imamoğlu A 2015 Nat. Phys. 11 141 Google Scholar
[42]	Aivazian G, Gong Z, Jones A M, Chu R L, Yan J, Mandrus D G, Zhang C, Cobden D, Yao W, Xu X 2015 Nat. Phys. 11 148 Google Scholar
[43]	Xu X, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343 Google Scholar
[44]	MacNeill D, Heikes C, Mak K F, Anderson Z, Kormányos A, Zólyomi V, Park J, Ralph D C 2015 Phys. Rev. Lett. 114 037401 Google Scholar
[45]	Ye Y, Xiao J, Wang H, Ye Z, Zhu H, Zhao M, Wang Y, Zhao J, Yin X, Zhang X 2016 Nat. Nanotechnol. 11 598 Google Scholar
[46]	Cracknell A P1975 Magnetism in Crystalline Materials (1st Ed.) (Oxford: Pergamon Press)
[47]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[48]	Zeng H, Dai J, Yao W, Xiao D, Cui X 2012 Nat. Nanotechnol. 7 490 Google Scholar
[49]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[50]	Weng H, Yu R, Hu X, Dai X, Fang Z 2015 Adv. Phys. 64 227 Google Scholar
[51]	de Juan F, Grushin A G, Morimoto T, Moore J E 2017 Nat. Commun. 8 15995 Google Scholar
[52]	You J S, Fang S, Xu S Y, Kaxiras E, Low T 2018 Phys. Rev. B 98 121109R Google Scholar
[53]	Zhang Y, Brink J van den, Felser C, Yan B 2018 2D Mater. 5 044001
[54]	Shi L, Song J C W 2019 Phys. Rev. B 99 035403 Google Scholar
[55]	Tian Y, Li Y, Jin X 2009 Phys. Rev. Lett. 103 087206 Google Scholar
[56]	Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, Deviatov E V 2019 JETP Lett. 109 715 Google Scholar
[57]	Huang M, Wu Z, Hu J, Cai X, Li E, An L, Feng X, Ye Z, Lin N, Law K T, Wang N 2020 arXiv: 2006.05615 [cond-mat.mes-hall]
[58]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji ZQ, Feng Y, Ji S, Chen X, Jia J, Dai X, Fang Z, Zhang S C, He K, Wang Y, Lu L, Ma X C, Xue Q K 2013 Science 340 167 Google Scholar
[59]	刘健鹏, 戴希 2020 69 147301 Google Scholar Liu J P, Dai X 2020 Acta Phys. Sin. 69 147301 Google Scholar
[60]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[61]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C and Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[62]	Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F 2020 Nature 579 56 Google Scholar
[63]	Chen S, He M, Zhang Y H, Hsieh V, Fei Z, Watanabe K, Taniguchi T, Cobden D H, Xu X, Dean C R, Yankowitz M 2020 Nat. Phys. 17 374
[64]	Polshyn H, Zhu J, Kumar M A, Zhang Y, Yang F, Tschirhart C L, Serlin M, Watanabe K, Taniguchi T, MacDonald A H, Young A F 2020 Nature 588 66 Google Scholar
[65]	Zhu J, Su J J, MacDonald A H 2020 Phys. Rev. Lett. 125 227702 Google Scholar
[66]	Cao Y, Luo J Y, Fatemi V, Fang S, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2016 Phys. Rev. Lett. 117 116804 Google Scholar
[67]	Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F, Dean C R 2019 Science 363 1059 Google Scholar
[68]	Kerelsky A, McGilly L J, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A, Pasupathy A N 2019 Nature 572 95 Google Scholar
[69]	Choi Y, Kemmer J, Peng Y, Thomson A, Arora H, Polski R, Zhang Y, Ren H, Alicea J, Refael G, von Oppen F, Watanabe K, Taniguchi T, Nadj-Perge S 2019 Nat. Phys. 15 1174 Google Scholar
[70]	Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237 Google Scholar
[71]	Lee D S, Riedl C, Beringer T, Castro Neto A H, von Klitzing K, Starke U, Smet J H 2011 Phys. Rev. Lett. 107 216602 Google Scholar
[72]	Kim Y, Park J, Song I, Ok J M, Jo Y, Watanabe K, Taniquchi T, Choi H C, Lee D S, Jung S, Kim J S 2016 Sci. Rep. 6 38068 Google Scholar
[73]	Moon P, Koshino M 2012 Phys. Rev. B 85 195458 Google Scholar
[74]	He W Y, Goldhaber-Gordon D, Law K T 2020 Nat. Commun. 11 1650 Google Scholar
[75]	He W Y, Law K T 2020 Phys. Rev. Res. 2 012073 Google Scholar
[76]	Liu Y, Shao Q 2020 ACS Nano 14 9389 Google Scholar
[77]	Xie M, MacDonald A H 2020 Phys. Rev. Lett. 124 097601 Google Scholar
[78]	Bultinck N, Chatterjee S, Zaletel M P 2020 Phys. Rev. Lett. 124 166601 Google Scholar
[79]	Peng R, Ma Y, Xu X, He Z, Huang B, Dai Y 2020 Phys. Rev. B 102 035412 Google Scholar
[80]	Ma Y, Kou L, Du A, Huang B, Dai Y, Heine T 2018 Phys. Rev. B 97 035444 Google Scholar
[81]	Xu Z, Zhang Q, Shen Q, Cheng Y, Schwingenschlögl U, Huang W 2017 J. Mater. Chem. C 5 10427 Google Scholar
[82]	Fu L 2009 Phys. Rev. Lett. 103 266801 Google Scholar
[83]	Alpichshev Z, Analytis J G, Chu J H, Fisher I R, Chen Y L, Shen Z X, Fang A, Kapitulnik A 2010 Phys. Rev. Lett. 104 016401 Google Scholar
[84]	Hosur P 2011 Phys. Rev. B 83 035309 Google Scholar
[85]	Zheng Z, Ma Q, Bi Z, de la Barrera S, Liu M H, Mao N, Zhang Y, Kiper N, Watanabe K, Taniguchi T, Kong J, Tisdale W A, Ashoori R, Gedik N, Fu L, Xu S Y, Jarillo-Herrero P 2020 Nature 588 71 Google Scholar

[1]	Jiang Long-Xing, Li Qing-Chao, Zhang Xu, Li Jing-Feng, Zhang Jing, Chen Zu-Xin, Zeng Min, Wu Hao. Spintronic devices based on topological and two-dimensional materials. Acta Physica Sinica, 2024, 73(1): 017505. doi: 10.7498/aps.73.20231166
[2]	Yu Ze-Hao, Zhang Li-Fa, Wu Jing, Zhao Yun-Shan. Recent progress of 2-dimensional layered thermoelectric materials. Acta Physica Sinica, 2023, 72(5): 057301. doi: 10.7498/aps.72.20222095
[3]	Bao Chang-Hua, Fan Ben-Shu, Tang Pei-Zhe, Duan Wen-Hui, Zhou Shu-Yun. Floquet engineering in quantum materials. Acta Physica Sinica, 2023, 72(23): 234202. doi: 10.7498/aps.72.20231423
[4]	Duan Xiu-Ming, Yi Zhi-Jun. Theoretical study on regulatory mechanism of dielectric environmental screening effects on binding energy of two-dimensional InX (X = Se, Te) exciton. Acta Physica Sinica, 2023, 72(14): 147102. doi: 10.7498/aps.72.20230528
[5]	Wu Ze-Fei, Huang Mei-Zhen, Wang Ning. Nonlinear Hall effects in two-dimensional moiré superlattices. Acta Physica Sinica, 2023, 72(23): 237301. doi: 10.7498/aps.72.20231324
[6]	Chen Xiao-Juan, Xu Kang, Zhang Xiu, Liu Hai-Yun, Xiong Qi-Hua. Research progress of bulk photovoltaic effect in two-dimensional materials. Acta Physica Sinica, 2023, 72(23): 237201. doi: 10.7498/aps.72.20231786
[7]	Tian Jin-Peng, Wang Shuo-Pei, Shi Dong-Xia, Zhang Guang-Yu. Vertical short-channel MoS₂ field-effect transistors. Acta Physica Sinica, 2022, 71(21): 218502. doi: 10.7498/aps.71.20220738
[8]	Song Rui, Wang Bi-Li, Feng Kai, Wang Li, Liang Dan-Dan. Structural, magnetic and ferroelectric properties of VOBr₂monolayer: A first-principles study. Acta Physica Sinica, 2022, 71(3): 037101. doi: 10.7498/aps.71.20211516
[9]	. Structural, magnetic and ferroelectric properties of VOBr2 monolayer: A first-principles study. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211516
[10]	Jiang Xiao-Hong, Qin Si-Chen, Xing Zi-Yue, Zou Xing-Yu, Deng Yi-Fan, Wang Wei, Wang Lin. Study on physical properties and magnetism controlling of two-dimensional magnetic materials. Acta Physica Sinica, 2021, 70(12): 127801. doi: 10.7498/aps.70.20202146
[11]	He Cong-Li, Xu Hong-Jun, Tang Jian, Wang Xiao, Wei Jin-Wu, Shen Shi-Peng, Chen Qing-Qiang, Shao Qi-Ming, Yu Guo-Qiang, Zhang Guang-Yu, Wang Shou-Guo. Research progress of spin-orbit torques based on two-dimensional materials. Acta Physica Sinica, 2021, 70(12): 127501. doi: 10.7498/aps.70.20210004
[12]	Wu Xiang-Shui, Tang Wen-Ting, Xu Xiang-Fan. Recent progresses of thermal conduction in two-dimensional materials. Acta Physica Sinica, 2020, 69(19): 196602. doi: 10.7498/aps.69.20200709
[13]	Liu Jian-Peng, Dai Xi. Topological properties and orbital magnetism in twisted graphene systems. Acta Physica Sinica, 2020, 69(14): 147301. doi: 10.7498/aps.69.20200506
[14]	Huang Bing-Quan, Zhou Tie-Ge, Wu Dao-Xiong, Zhang Zhao-Fu, Li Bai-Kui. Properties of vacancies and N-doping in monolayer g-ZnO: First-principles calculation and molecular orbital theory analysis. Acta Physica Sinica, 2019, 68(24): 246301. doi: 10.7498/aps.68.20191258
[15]	Liu Qi-Neng. The defect mode and the quantum effect of light wave in cylindrical anisotropic photonic crystal. Acta Physica Sinica, 2011, 60(1): 014217. doi: 10.7498/aps.60.014217
[16]	Yuan Ning-Yi, Chen Xiao-Shuang, Ding Jian-Ning, He Ze-Jun, Li Feng, Lu Wei. Quantum effect and up-conversion luminescence of ZnO-SiO2 composite films synthesized by sol-gel technique. Acta Physica Sinica, 2009, 58(4): 2649-2653. doi: 10.7498/aps.58.2649
[17]	Liu Kui, Ding Hong-Lin, Zhang Xian-Gao, Yu Lin-Wei, Huang Xin-Fan, Chen Kun-Ji. Simulation of a triple-gate single electron FET memory with a quantum dot floating gate and a quantum wire channel. Acta Physica Sinica, 2008, 57(11): 7052-7056. doi: 10.7498/aps.57.7052
[18]	Wang Yue-Yue, Yang Qin, Dai Chao-Qing, Zhang Jie-Fang. Solitary wave solution of Zakharov equation with quantum effect. Acta Physica Sinica, 2006, 55(3): 1029-1034. doi: 10.7498/aps.55.1029
[19]	Li Yan-Ping, Xu Jing-Ping, Chen Wei-Bing, Xu Sheng-Guo, Ji Feng. 2-D threshold voltage model for short-channel MOSFET with quantum-mechanical effects. Acta Physica Sinica, 2006, 55(7): 3670-3676. doi: 10.7498/aps.55.3670
[20]	Dai Yue-Hua, Chen Jun-Ning, Ke Dao-Ming, Sun Jia-E. An analytical model of MOSFET threshold voltage with considiring the quantum effects. Acta Physica Sinica, 2005, 54(2): 897-901. doi: 10.7498/aps.54.897

Catalog

Vol. 70, Issue 12 - 2021-06-20

Metrics

Abstract views: 11292
PDF Downloads: 973
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板