转角二维量子材料中平带相关的新奇电子态物性

王仲锐; 姜宇航

doi:10.7498/aps.71.20220064

摘要

二维量子材料具有诸多新奇的电子态物性, 又易受到外部因素的影响和调控, 因此成为近年来凝聚态物理等研究领域的前沿课题之一. 而当以不同的旋转角度和堆叠次序制备出二维量子材料的异质结时, 莫尔超晶格的形成又进一步诱导了异质结电子能带结构的重整化, 从而形成电子平带结构, 再结合外加电场、磁场、应力场等外部条件, 即可实现对材料整体新奇物性的设计与调控. 本文主要围绕转角石墨烯及过渡金属硫族化合物异质结中的相关研究展开讨论, 包括与平带物理相关的强关联效应、非常规超导现象、量子反常霍尔效应、拓扑相以及电子晶体等行为, 并对未来的研究发展进行了展望.

关键词:

Abstract

Two-dimensional (2D) materials can exhibit novel quantum phenomena and be easily tuned by the external environment, which has made them one of the most attractive topics in condensed matter physics during the recent decades. The moiré superlattice induced by varied stacking geometry can further renormalize the material band structure, resulting in the electronic flat bands. With the help of external fields, one can tune the electron-electron correlated interaction in these flat bands, even control the overall physical properties. In this paper we review the recent researches of novel properties in twisted 2D materials (graphene and transition metal dichalcogenide heterostructure), involving strong correlation effect, unconventional superconductivity, quantum anomalous Hall effect, topological phase, and electronic crystals. We also discuss some open questions and give further prospects in this field.

Keywords:

作者及机构信息

王仲锐¹,
姜宇航^1,2

1.
中国科学院大学材料科学与光电技术学院, 北京　100049

2.
中国科学院大学材料与光电研究中心, 北京　100049

通信作者: 姜宇航, yuhangjiang@ucas.ac.cn

基金项目: 国家自然科学基金(批准号: 12074377)和中央高校基本科研业务费专项资金资助的课题.

Authors and contacts

1.
College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China

2.
Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Jiang Yu-Hang, yuhangjiang@ucas.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12074377) and the Fundamental Research Funds for the Central Universities, China.

文章全文 : translate this paragraph

参考文献

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[3]	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, Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[4]	Li G, Luican A, Lopes dos Santos J M B, Castro Neto A H, Reina A, Kong J, Andrei E Y 2010 Nat. Phys. 6 109 Google Scholar
[5]	Yin L J, Qiao J B, Zuo W J, Li W T, He L 2015 Phys. Rev. B 92 081406 Google Scholar
[6]	Bistritzer R, MacDonald A H 2011 PNAS 108 12233 Google Scholar
[7]	Jiang Y H, Lai X Y, Watanabe K, Taniguchi T, Haule K, Mao J H, Andrei E Y 2019 Nature 573 91 Google Scholar
[8]	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
[9]	Xie Y L, Lian B, Jäck B, Liu X M, Chiu C L, Watanabe K, Taniguchi T, Bernevig B A, Yazdani A 2019 Nature 572 101 Google Scholar
[10]	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
[11]	Hao Z Y, Zimmerman A M, Ledwith P, Khalaf E, Najafabadi Danial H, Watanabe K, Taniguchi T, Vishwanath A, Kim P 2021 Science 371 1133 Google Scholar
[12]	Jiao L, Howard S, Ran S, Wang Z Y, Rodriguez J O, Sigrist M, Wang Z Q, Butch N P, Madhavan V 2020 Nature 579 523 Google Scholar
[13]	Falson J, Xu Y, Liao M H, Zang Y Y, Zhu K, Wang C, Zhang Z, Liu H C, Duan W H, He K, Liu H W, Smet J H, Zhang D, Xue Q K 2020 Science 367 1454 Google Scholar
[14]	Choi Y J, Kim H, Peng Y, Thomson A, Lewandowski C, Polski R, Zhang Y R, Arora H S, Watanabe K, Taniguchi T, Alicea J, Nadj-Perge S 2021 Nature 589 536 Google Scholar
[15]	Nuckolls K P, Oh M, Wong D, Lian B, Watanabe K, Taniguchi T, Bernevig B A, Yazdani A 2020 Nature 588 610 Google Scholar
[16]	Chen Q Y, Luo X B, Xie D H, Li M L, Ji X Y, Zhou R, Huang Y B, Zhang W, Feng W, Zhang Y, Huang L, Hao Q Q, Liu Q, Zhu X G, Liu Y, Zhang P, Lai X C, Si Q, Tan S Y 2019 Phys. Rev. Lett. 123 106402 Google Scholar
[17]	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 2021 Nat. Phys. 17 374 Google Scholar
[18]	Li H Y, Li S W, Regan E C, Wang D Q, Zhao W Y, Kahn S, Yumigeta K, Blei M, Taniguchi T, Watanabe K, Tongay S, Zettl A, Crommie M F, Wang F 2021 Nature 597 650 Google Scholar
[19]	Smoleński T, Dolgirev P E, Kuhlenkamp C, Popert A, Shimazaki Y, Back P, Lu X, Kroner M, Watanabe K, Taniguchi T, Esterlis I, Demler E, Imamoğlu A 2021 Nature 595 53 Google Scholar
[20]	Zhou Y, Sung J, Brutschea E, Esterlis I, Wang Y, Scuri G, Gelly R J, Heo H, Taniguchi T, Watanabe K, Zaránd G, Lukin M D, Kim P, Demler E, Park H 2021 Nature 595 48 Google Scholar
[21]	Andrei E Y, MacDonald A H 2020 Nat. Mater. 19 1265 Google Scholar
[22]	Yankowitz M, Xue J M, Cormode D, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P, LeRoy B J 2012 Nat. Phys. 8 382 Google Scholar
[23]	Andrei E Y, Li G, Du X 2012 Rep. Prog. Phys. 75 056501 Google Scholar
[24]	Brihuega I, Mallet P, González-Herrero H, Trambly de Laissardière G, Ugeda M M, Magaud L, Gómez-Rodríguez J M, Ynduráin F, Veuillen J Y 2012 Phys. Rev. Lett. 109 196802 Google Scholar
[25]	Lu X B, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G Y, Bachtold A, MacDonald A H, Efetov D K 2019 Nature 574 653 Google Scholar
[26]	Cong C X, Yu T 2014 Nat. Commun. 5 4709 Google Scholar
[27]	Kim K, Yankowitz M, Fallahazad B, Kang S, Movva H C P, Huang S Q, Larentis S, Corbet C M, Taniguchi T, Watanabe K, Banerjee S K, LeRoy B J, Tutuc E 2016 Nano Lett. 16 1989 Google Scholar
[28]	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
[29]	Chen G R, Jiang L L, Wu S, Lyu B S, Li H Y, Chittari B L, Watanabe K, Taniguchi T, Shi Z W, Jung J, Zhang Y B, Wang F 2019 Nat. Phys. 15 237 Google Scholar
[30]	Chen G R, Sharpe A L, Gallagher P, Rosen I T, Fox E J, Jiang L L, Lyu B S, Li H Y, Watanabe K, Taniguchi T, Jung J, Shi Z, Goldhaber-Gordon D, Zhang Y B, Wang F 2019 Nature 572 215 Google Scholar
[31]	Mao J H, Milovanović S P, Anđelković M, Lai X Y, Cao Y, Watanabe K, Taniguchi T, Covaci L, Peeters F M, Geim A K, Jiang Y H, Andrei E Y 2020 Nature 584 215 Google Scholar
[32]	Shen C, Chu Y B, Wu Q S, Li N, Wang S P, Zhao Y C, Tang J, Liu J Y, Tian J P, Watanabe K, Taniguchi T, Yang R, Meng Z Y, Shi D X, Yazyev O V, Zhang G Y 2020 Nat. Phys. 16 520 Google Scholar
[33]	Stepanov P, Das I, Lu X B, Fahimniya A, Watanabe K, Taniguchi T, Koppens F H L, Lischner J, Levitov L, Efetov D K 2020 Nature 583 375 Google Scholar
[34]	Arora H S, Polski R, Zhang Y, Thomson A, Choi Y J, Kim H, Lin Z, Wilson I Z, Xu X D, Chu J H, Watanabe K, Taniguchi T, Alicea J, Nadj-Perge S 2020 Nature 583 379 Google Scholar
[35]	Saito Y, Ge J Y, Watanabe K, Taniguchi T, Young A F 2020 Nat. Phys. 16 926 Google Scholar
[36]	Berdyugin A I, Xu S G, Pellegrino F M D, Kumar R K, Principi A, Torre I, Shalom M B, Taniguchi T, Watanabe K, Grigorieva I V, Polini M, Geim A K, Bandurin D A 2019 Science 364 162 Google Scholar
[37]	Gallagher P, Yang C S, Lyu T, Tian F L, Kou R, Zhang H, Watanabe K, Taniguchi T, Wang F 2019 Science 364 158 Google Scholar
[38]	Lian B, Wang Z, Bernevig B A 2019 Phys. Rev. Lett. 122 257002 Google Scholar
[39]	Choi Y W, Choi H J 2018 Phys. Rev. B 98 241412 Google Scholar
[40]	Oh M, Nuckolls K P, Wong D, Lee R L, Liu X M, Watanabe K, Taniguchi T, Yazdani A 2021 Nature 600 240 Google Scholar
[41]	Park J M, Cao Y, Watanabe K, Taniguchi T, Jarillo-Herrero P 2021 Nature 590 249 Google Scholar
[42]	Zhou H X, Xie T, Taniguchi T, Watanabe K, Young A F 2021 Nature 598 434 Google Scholar
[43]	Zhou H X, Xie T, Ghazaryan A, Holder T, Ehrets J R, Spanton E M, Taniguchi T, Watanabe K, Berg E, Serbyn M, Young A F 2021 Nature 598 429 Google Scholar
[44]	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
[45]	Liu J P, Dai X 2021 Phys. Rev. B 103 035427 Google Scholar
[46]	Pixley J H, Andrei E Y 2019 Science 365 543 Google Scholar
[47]	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
[48]	Wu S, Zhang Z Y, Watanabe K, Taniguchi T, Andrei E Y 2021 Nat. Mater. 20 488 Google Scholar
[49]	Saito Y, Ge J Y, Rademaker L, Watanabe K, Taniguchi T, Abanin D A, Young A F 2021 Nat. Phys. 17 478 Google Scholar
[50]	Gao X G, Li X K, Xin W, Chen X D, Liu Z B, Tian J G 2020 Nanophotonics 9 1717 Google Scholar
[51]	Zhang Z M, Wang Y M, Watanabe K, Taniguchi T, Ueno K, Tutuc E, LeRoy B J 2020 Nat. Phys. 16 1093 Google Scholar
[52]	Li H Y, Li S W, Naik M H, Xie J X, Li X Y, Wang J Y, Regan E, Wang D Q, Zhao W Y, Zhao S H, Kahn S, Yumigeta K, Blei M, Taniguchi T, Watanabe K, Tongay S, Zettl A, Louie S G, Wang F, Crommie M F 2021 Nat. Mater. 20 945 Google Scholar
[53]	Li H Y, Li S W, Naik M H, Xie J X, Li X Y, Regan E, Wang D Q, Zhao W Y, Yumigeta K, Blei M, Taniguchi T, Watanabe K, Tongay S, Zettl A, Louie S G, Crommie M F, Wang F 2021 Nat. Phys. 17 1114 Google Scholar
[54]	Xiao D, Liu G B, Feng W X, Xu X D, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[55]	Zhu Z Y, Cheng Y C, Schwingenschlögl U 2011 Phys. Rev. B 84 153402 Google Scholar
[56]	Zhao C, Norden T, Zhang P Y, Zhao P Q, Cheng Y C, Sun F, Parry J P, Taheri P, Wang J Q, Yang Y H, Scrace T, Kang K F, Yang S, Miao G X, Sabirianov R, Kioseoglou G, Huang W, Petrou A, Zeng H 2017 Nat. Nanotechnol. 12 757 Google Scholar
[57]	Wu Z F, Zhou B T, Cai X B, Cheung P, Liu G B, Huang M Z, Lin J X Z, Han T Y, An L H, Wang Y W, Xu S G, Long G, Cheng C, Law K T, Zhang F, Wang N 2019 Nat. Commun. 10 611 Google Scholar
[58]	Cui J, Li P L, Zhou J D, He W Y, Huang X W, Yi J, Fan J, Ji Z Q, Jing X N, Qu F M, Cheng Z G, Yang C L, Lu L, Suenaga K, Liu J W, Law K T, Lin J H, Liu Z, Liu G T 2019 Nat. Commun. 10 2044 Google Scholar
[59]	Naik M H, Jain M 2018 Phys. Rev. Lett. 121 266401 Google Scholar
[60]	Li E, Hu J X, Feng X M, Zhou Z S, An L H, Law K T, Wang N, Lin N 2021 Nat. Commun. 12 5601 Google Scholar
[61]	Wu F C, Lovorn T, Tutuc E, MacDonald A H 2018 Phys. Rev. Lett. 121 026402 Google Scholar
[62]	Koshino M, Yuan N F Q, Koretsune T, Ochi M, Kuroki K, Fu L 2018 Phys. Rev. X 8 031087 Google Scholar
[63]	Wu F C, Lovorn T, Tutuc E, Martin I, MacDonald A H 2019 Phys. Rev. Lett. 122 086402 Google Scholar
[64]	Wang L, Shih E M, Ghiotto A, Xian L D, Rhodes D A, Tan C, Claassen M, Kennes D M, Bai Y S, Kim B, Watanabe K, Taniguchi T, Zhu X Y, Hone J, Rubio A, Pasupathy A N, Dean C R 2020 Nat. Mater. 19 861 Google Scholar
[65]	Tang Y H, Li L Z, Li T X, Xu Y, Liu S, Barmak K, Watanabe K, Taniguchi T, MacDonald A H, Shan J, Mak K F 2020 Nature 579 353 Google Scholar
[66]	Regan E C, Wang D Q, Jin C H, Bakti Utama M I, Gao B N, Wei X, Zhao S H, Zhao W Y, Zhang Z C, Yumigeta K, Blei M, Carlström J D, Watanabe K, Taniguchi T, Tongay S, Crommie M, Zettl A, Wang F 2020 Nature 579 359 Google Scholar
[67]	Huang X, Wang T M, Miao S N, Wang C, Li Z P, Lian Z, Taniguchi T, Watanabe K, Okamoto S, Xiao D, Shi S F, Cui Y T 2021 Nat. Phys. 17 715 Google Scholar
[68]	Jin C H, Tao Z, Li T X, Xu Y, Tang Y H, Zhu J C, Liu S, Watanabe K, Taniguchi T, Hone J C, Fu L, Shan J, Mak K F 2021 Nat. Mater. 20 940 Google Scholar
[69]	Chen J L, Lin X, Chen M Y, Low T, Chen H S, Dai S Y 2021 Appl. Phys. Lett. 119 240501 Google Scholar
[70]	Wu Z L, Liu Y R, Hill E H, Zheng Y B 2018 Nanoscale 10 18096 Google Scholar
[71]	Zhang X Y, Zhong Y H, Low T, Chen H S, Lin X 2021 Phys. Rev. B 103 195405 Google Scholar
[72]	Mao X R, Shao Z K, Luan H Y, Wang S L, Ma R M 2021 Nat. Nanotechnol. 16 1099 Google Scholar
[73]	Jin C H, Regan E C, Yan A M, Iqbal Bakti Utama M, Wang D Q, Zhao S H, Qin Y, Yang S J, Zheng Z R, Shi S Y, Watanabe K, Taniguchi T, Tongay S, Zettl A, Wang F 2019 Nature 567 76 Google Scholar
[74]	Ahn S J, Moon P, Kim T H, Kim H W, Shin H C, Kim E H, Cha H W, Kahng S J, Kim P, Koshino M, Son Y W, Yang C W, Ahn J R 2018 Science 361 782 Google Scholar
[75]	González J, Stauber T 2020 Phys. Rev. Lett. 124 186801 Google Scholar

施引文献

图 1 (a) 单层石墨烯低能区线性能带结构^[21]; (b) 转角石墨烯形成的莫尔超晶格^[21]; (c) STM观测TBG的示意图与均匀的莫尔斑点^[21]; (d) 转角石墨烯电子能带结构^[3]; (e) 原位解理-转移制备法^[27]; (f) 第一布里渊区中的平带体系^[2]

Fig. 1. (a) Low-energy band structure of monolayer graphene^[21]; (b) moiré pattern formed by twisted graphene^[21]; (c) schematics of STM measurement of TBG sample, topography of which shows a uniform moiré pattern^[21]; (d) band structure of twisted graphene^[3]; (e) tear-and-stack technique^[27]; (f) flat band structure in the first Brillouin zone^[2].

下载: 全尺寸图片幻灯片

图 2 转角石墨烯体系中平带相关的关联绝缘态　(a) T = 0.3 K时, 魔角石墨烯电导率随载流子浓度的变化^[3]; (b) 从0 T(黑色曲线)到480 mT(红色曲线)不同垂直磁场下纵向电阻随载流子浓度的变化^[25]; (c) 由hBN封装的双栅极ABC-TLG侧向示意图^[29]; (d) ABC-TLG电阻随V_t和V_b的变化(颜色从亮到暗代表电阻从100 kΩ到10 Ω, V_t和V_b分别代表顶部栅压与底部栅压)^[29]; (e) 魔角石墨烯中电荷条纹有序相^[7]; (f) T = 0.3 K, θ = 1.08°时, TMBG的电阻率随电位移场D与载流子浓度的变化^[17]; (g) D < 0时, ν = 1, 2, 3处的关联态性质^[17]

Fig. 2. Correlated insulating state of flat band in twisted graphene system: (a) measured conductance of magic-angle graphene as a function of carrier density at T = 0.3 K^[3]; (b) longitudinal resistance against carrier density at different perpendicular magnetic fields from 0 T (black trace) to 480 mT (red trace) ^[25]; (c) schematic cross-sectional view of the dual-gated ABC-TLG device encapsulated by hBN^[29]; (d) ABC-TLG resistance as a function of V_t and V_b (The colour scale is from 10 Ω (dark) to 100 kΩ (bright) in a log scale, V_t and V_b refer to the top and bottom gate voltage)^[29]; (e) stripe charge ordered phase in magic-angle graphene^[7]; (f) resistivity of TMBG plotted against electric displacement field D and carrier density under the condition of T = 0.3 K and θ = 1.08°^[17]; (g) properties of the correlated states at ν= 1, 2, 3 for D < 0^[17].

下载: 全尺寸图片幻灯片

图 3 魔角石墨烯非常规超导态　(a), (b) 电阻与温度和载流子浓度的关系, 显示出魔角石墨烯在(a) 半填充^[2]和(b) 整数填充^[25]绝缘态附近的超导圆顶; (c) 三个屏蔽调控的魔角石墨烯电阻与温度和填充因子关系, 在整数填充附近呈现关联绝缘态消失的超导特征^[33]; 利用Dynes方程对(d) s波超导体和(e)节点超导体的准粒子态密度模型进行实验谱学上的模拟^[40]; (f) 过剩电流、超导能隙与温度的关系^[40]; (g) 相对霍尔密度 $ \left|{n}_{\mathrm{H}}-\nu \right| $随载流子浓度和电位移场的变化^[11]

Fig. 3. Unconventional superconductivity of magic-angle graphene: (a), (b) Resistance as a function of temperature and carrier density, where shows superconductivity domes around (a) half-filling^[2] and (b) integer-filling^[25] correlated states of magic-angle graphene respectively; (c) colour plot of resistivity versus moiré band filling factor ν and temperature for three screening-controlled magic-angle TBG devices, which shows correlated insulators are completely absent, while superconductivity persists^[33]; Dynes-function fits to the experimental tunneling spectrum using the model quasiparticle density of states for (d) s-wave superconductor and (e) nodal superconductor^[40]; (f) excess current and the superconducting energy gap versus temperature^[40]; (g) subtracted Hall density $ \left|{n}_{\mathrm{H}}-\nu \right| $ as a function of carrier density and electric displacement field^[11].

下载: 全尺寸图片幻灯片

图 4 转角石墨烯的量子反常霍尔效应　(a) 30 mK下, 3/4填充魔角石墨烯霍尔电阻随磁场的变化; (b) θ = 1.20°± 0.01°时, 不同温度下3/4填充魔角石墨烯霍尔电阻随磁场的变化^[44]; (c) 魔角石墨烯铁磁性拓扑绝缘性质示意图^[46]; (d) 强关联Chern绝缘体对磁场的量子化响应^[15]; (e) T = 0.3 K, n/n₀ = 3.5时, 纵向电阻R*与平面内磁场B_∥的关系^[48]; (f) Chern绝缘体示意图, 红线对应于(t, s) = (–2, –3/2)和(–3, –1/2)的对称破缺Chern绝缘体(s是布洛赫带填充指数; t是与带隙相关的总Chern数)^[49]

Fig. 4. Anomalous Hall Effect of magic-angle graphene: (a) Hall resistance of twisted graphene tested as a function of magnetic fields at 30 mK near three-quarters filling; (b) Hall resistance of twisted graphene tested as a function of magnetic fields at different temperatures near three-quarters filling at θ = 1.20°±0.01°^[44]; (c) schematic of the ferromagnetic topological insulator property of magic-angle graphene^[46]; (d) quantized magnetic-field response of strongly correlated Chern insulating phases^[15]; (e) in-plane field B_∥ dependence of longitudinal R*, at n/n₀= 3.5, at T = 0.3 K^[48]; (f) schematic of Chern insulator states, with red lines corresponding to SBCIs with (t, s) = (–2, –3/2) and (–3, –1/2)( s is the Bloch band filling index; t is the total Chern number associated with a given gap) ^[49].

下载: 全尺寸图片幻灯片

图 5 (a)—(c) 不同转角双层WSe₂的STS分析^[60]; (d)—(f) WSe₂/WS₂异质结莫尔超晶格重构^[52]

Fig. 5. (a)–(c) STS of twisted bilayer-WSe₂ with different twisted angles^[60]; (d)–(f) moiré superlattice reconstruction of WSe₂/WS₂ heterostructure^[52].

下载: 全尺寸图片幻灯片

图 6 (a) 转角WSe₂异质结示意图与莫尔超晶格平带结构^[64]; (b) 电阻随温度和载流子浓度变化的相图(D = 0.45 V/nm, θ = 5.1°, 顶部栅压V_tg = –12.25 V)^[64]; (c), (d) 转角与电位移场共同调制的关联绝缘态^[64]; (e) WS₂/WSe₂异质结器件结构示意图^[67]; (f) 2.8—140 K时的关联绝缘态以及晶格填充情况的蒙特卡罗模拟^[67]

Fig. 6. (a) Schematic of the twisted bilayer-WSe₂ sample and the moiré superlattice flat bands structure ^[64]; (b) resistance color plotted against temperature and carrier density (D = 0.45 V/nm, θ = 5.1°, top gate V_tg = –12.25 V)^[64]; (c), (d) angle and electric displacement field dependence of the correlated insulating states^[64]; (e) schematic of the WS₂/WSe₂ device structure ^[67]; (f) correlated insulating states at a temperature range from 2.8 K to 140 K and spatial filling patterns gained from Monte Carlo simulation^[67]

下载: 全尺寸图片幻灯片

图 7 4%晶格错配WSe₂/WS₂ 莫尔超晶格　(a) 光学各向异性测量示意图^[68]; (b) 1/2填充时电子条纹的结构域图^[68]; (c) WSe₂/WS₂ 异质结示意图及广义Wigner晶格^[18]; (d) 双层MoSe₂中Wigner晶体的量子与温度相变^[20]; (e) 不同栅压下Se/W 莫尔位点的dI/dV谱, 显示出 STM针尖在莫尔周期里的局部放电现象(蓝色箭头表示充放电时表面色散特征)^[53]

Fig. 7. 4% mismatch WSe₂/WS₂ moiré superlattice: (a) Schematics of optical anisotropy measurement^[68]; (b) electronic stripe domain patterns at half filling^[68]; (c) schematic of correlated states and generalized Wigner crystal states in a WSe₂/WS₂ moiré superlattice^[18]; (d) MoSe₂ bilayer Wigner crystals’ quantum and thermal phase transitions^[20]; (e) gate-dependent dI/dV spectra measured at the Se/W moiré sites, showing local discharging of moiré site induced by the STM tip (The blue arrows indicate surface dispersion characteristics during charge and discharge)^[53].

下载: 全尺寸图片幻灯片

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43 Google Scholar
[3]	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, Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[4]	Li G, Luican A, Lopes dos Santos J M B, Castro Neto A H, Reina A, Kong J, Andrei E Y 2010 Nat. Phys. 6 109 Google Scholar
[5]	Yin L J, Qiao J B, Zuo W J, Li W T, He L 2015 Phys. Rev. B 92 081406 Google Scholar
[6]	Bistritzer R, MacDonald A H 2011 PNAS 108 12233 Google Scholar
[7]	Jiang Y H, Lai X Y, Watanabe K, Taniguchi T, Haule K, Mao J H, Andrei E Y 2019 Nature 573 91 Google Scholar
[8]	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
[9]	Xie Y L, Lian B, Jäck B, Liu X M, Chiu C L, Watanabe K, Taniguchi T, Bernevig B A, Yazdani A 2019 Nature 572 101 Google Scholar
[10]	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
[11]	Hao Z Y, Zimmerman A M, Ledwith P, Khalaf E, Najafabadi Danial H, Watanabe K, Taniguchi T, Vishwanath A, Kim P 2021 Science 371 1133 Google Scholar
[12]	Jiao L, Howard S, Ran S, Wang Z Y, Rodriguez J O, Sigrist M, Wang Z Q, Butch N P, Madhavan V 2020 Nature 579 523 Google Scholar
[13]	Falson J, Xu Y, Liao M H, Zang Y Y, Zhu K, Wang C, Zhang Z, Liu H C, Duan W H, He K, Liu H W, Smet J H, Zhang D, Xue Q K 2020 Science 367 1454 Google Scholar
[14]	Choi Y J, Kim H, Peng Y, Thomson A, Lewandowski C, Polski R, Zhang Y R, Arora H S, Watanabe K, Taniguchi T, Alicea J, Nadj-Perge S 2021 Nature 589 536 Google Scholar
[15]	Nuckolls K P, Oh M, Wong D, Lian B, Watanabe K, Taniguchi T, Bernevig B A, Yazdani A 2020 Nature 588 610 Google Scholar
[16]	Chen Q Y, Luo X B, Xie D H, Li M L, Ji X Y, Zhou R, Huang Y B, Zhang W, Feng W, Zhang Y, Huang L, Hao Q Q, Liu Q, Zhu X G, Liu Y, Zhang P, Lai X C, Si Q, Tan S Y 2019 Phys. Rev. Lett. 123 106402 Google Scholar
[17]	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 2021 Nat. Phys. 17 374 Google Scholar
[18]	Li H Y, Li S W, Regan E C, Wang D Q, Zhao W Y, Kahn S, Yumigeta K, Blei M, Taniguchi T, Watanabe K, Tongay S, Zettl A, Crommie M F, Wang F 2021 Nature 597 650 Google Scholar
[19]	Smoleński T, Dolgirev P E, Kuhlenkamp C, Popert A, Shimazaki Y, Back P, Lu X, Kroner M, Watanabe K, Taniguchi T, Esterlis I, Demler E, Imamoğlu A 2021 Nature 595 53 Google Scholar
[20]	Zhou Y, Sung J, Brutschea E, Esterlis I, Wang Y, Scuri G, Gelly R J, Heo H, Taniguchi T, Watanabe K, Zaránd G, Lukin M D, Kim P, Demler E, Park H 2021 Nature 595 48 Google Scholar
[21]	Andrei E Y, MacDonald A H 2020 Nat. Mater. 19 1265 Google Scholar
[22]	Yankowitz M, Xue J M, Cormode D, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P, LeRoy B J 2012 Nat. Phys. 8 382 Google Scholar
[23]	Andrei E Y, Li G, Du X 2012 Rep. Prog. Phys. 75 056501 Google Scholar
[24]	Brihuega I, Mallet P, González-Herrero H, Trambly de Laissardière G, Ugeda M M, Magaud L, Gómez-Rodríguez J M, Ynduráin F, Veuillen J Y 2012 Phys. Rev. Lett. 109 196802 Google Scholar
[25]	Lu X B, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G Y, Bachtold A, MacDonald A H, Efetov D K 2019 Nature 574 653 Google Scholar
[26]	Cong C X, Yu T 2014 Nat. Commun. 5 4709 Google Scholar
[27]	Kim K, Yankowitz M, Fallahazad B, Kang S, Movva H C P, Huang S Q, Larentis S, Corbet C M, Taniguchi T, Watanabe K, Banerjee S K, LeRoy B J, Tutuc E 2016 Nano Lett. 16 1989 Google Scholar
[28]	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
[29]	Chen G R, Jiang L L, Wu S, Lyu B S, Li H Y, Chittari B L, Watanabe K, Taniguchi T, Shi Z W, Jung J, Zhang Y B, Wang F 2019 Nat. Phys. 15 237 Google Scholar
[30]	Chen G R, Sharpe A L, Gallagher P, Rosen I T, Fox E J, Jiang L L, Lyu B S, Li H Y, Watanabe K, Taniguchi T, Jung J, Shi Z, Goldhaber-Gordon D, Zhang Y B, Wang F 2019 Nature 572 215 Google Scholar
[31]	Mao J H, Milovanović S P, Anđelković M, Lai X Y, Cao Y, Watanabe K, Taniguchi T, Covaci L, Peeters F M, Geim A K, Jiang Y H, Andrei E Y 2020 Nature 584 215 Google Scholar
[32]	Shen C, Chu Y B, Wu Q S, Li N, Wang S P, Zhao Y C, Tang J, Liu J Y, Tian J P, Watanabe K, Taniguchi T, Yang R, Meng Z Y, Shi D X, Yazyev O V, Zhang G Y 2020 Nat. Phys. 16 520 Google Scholar
[33]	Stepanov P, Das I, Lu X B, Fahimniya A, Watanabe K, Taniguchi T, Koppens F H L, Lischner J, Levitov L, Efetov D K 2020 Nature 583 375 Google Scholar
[34]	Arora H S, Polski R, Zhang Y, Thomson A, Choi Y J, Kim H, Lin Z, Wilson I Z, Xu X D, Chu J H, Watanabe K, Taniguchi T, Alicea J, Nadj-Perge S 2020 Nature 583 379 Google Scholar
[35]	Saito Y, Ge J Y, Watanabe K, Taniguchi T, Young A F 2020 Nat. Phys. 16 926 Google Scholar
[36]	Berdyugin A I, Xu S G, Pellegrino F M D, Kumar R K, Principi A, Torre I, Shalom M B, Taniguchi T, Watanabe K, Grigorieva I V, Polini M, Geim A K, Bandurin D A 2019 Science 364 162 Google Scholar
[37]	Gallagher P, Yang C S, Lyu T, Tian F L, Kou R, Zhang H, Watanabe K, Taniguchi T, Wang F 2019 Science 364 158 Google Scholar
[38]	Lian B, Wang Z, Bernevig B A 2019 Phys. Rev. Lett. 122 257002 Google Scholar
[39]	Choi Y W, Choi H J 2018 Phys. Rev. B 98 241412 Google Scholar
[40]	Oh M, Nuckolls K P, Wong D, Lee R L, Liu X M, Watanabe K, Taniguchi T, Yazdani A 2021 Nature 600 240 Google Scholar
[41]	Park J M, Cao Y, Watanabe K, Taniguchi T, Jarillo-Herrero P 2021 Nature 590 249 Google Scholar
[42]	Zhou H X, Xie T, Taniguchi T, Watanabe K, Young A F 2021 Nature 598 434 Google Scholar
[43]	Zhou H X, Xie T, Ghazaryan A, Holder T, Ehrets J R, Spanton E M, Taniguchi T, Watanabe K, Berg E, Serbyn M, Young A F 2021 Nature 598 429 Google Scholar
[44]	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
[45]	Liu J P, Dai X 2021 Phys. Rev. B 103 035427 Google Scholar
[46]	Pixley J H, Andrei E Y 2019 Science 365 543 Google Scholar
[47]	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
[48]	Wu S, Zhang Z Y, Watanabe K, Taniguchi T, Andrei E Y 2021 Nat. Mater. 20 488 Google Scholar
[49]	Saito Y, Ge J Y, Rademaker L, Watanabe K, Taniguchi T, Abanin D A, Young A F 2021 Nat. Phys. 17 478 Google Scholar
[50]	Gao X G, Li X K, Xin W, Chen X D, Liu Z B, Tian J G 2020 Nanophotonics 9 1717 Google Scholar
[51]	Zhang Z M, Wang Y M, Watanabe K, Taniguchi T, Ueno K, Tutuc E, LeRoy B J 2020 Nat. Phys. 16 1093 Google Scholar
[52]	Li H Y, Li S W, Naik M H, Xie J X, Li X Y, Wang J Y, Regan E, Wang D Q, Zhao W Y, Zhao S H, Kahn S, Yumigeta K, Blei M, Taniguchi T, Watanabe K, Tongay S, Zettl A, Louie S G, Wang F, Crommie M F 2021 Nat. Mater. 20 945 Google Scholar
[53]	Li H Y, Li S W, Naik M H, Xie J X, Li X Y, Regan E, Wang D Q, Zhao W Y, Yumigeta K, Blei M, Taniguchi T, Watanabe K, Tongay S, Zettl A, Louie S G, Crommie M F, Wang F 2021 Nat. Phys. 17 1114 Google Scholar
[54]	Xiao D, Liu G B, Feng W X, Xu X D, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[55]	Zhu Z Y, Cheng Y C, Schwingenschlögl U 2011 Phys. Rev. B 84 153402 Google Scholar
[56]	Zhao C, Norden T, Zhang P Y, Zhao P Q, Cheng Y C, Sun F, Parry J P, Taheri P, Wang J Q, Yang Y H, Scrace T, Kang K F, Yang S, Miao G X, Sabirianov R, Kioseoglou G, Huang W, Petrou A, Zeng H 2017 Nat. Nanotechnol. 12 757 Google Scholar
[57]	Wu Z F, Zhou B T, Cai X B, Cheung P, Liu G B, Huang M Z, Lin J X Z, Han T Y, An L H, Wang Y W, Xu S G, Long G, Cheng C, Law K T, Zhang F, Wang N 2019 Nat. Commun. 10 611 Google Scholar
[58]	Cui J, Li P L, Zhou J D, He W Y, Huang X W, Yi J, Fan J, Ji Z Q, Jing X N, Qu F M, Cheng Z G, Yang C L, Lu L, Suenaga K, Liu J W, Law K T, Lin J H, Liu Z, Liu G T 2019 Nat. Commun. 10 2044 Google Scholar
[59]	Naik M H, Jain M 2018 Phys. Rev. Lett. 121 266401 Google Scholar
[60]	Li E, Hu J X, Feng X M, Zhou Z S, An L H, Law K T, Wang N, Lin N 2021 Nat. Commun. 12 5601 Google Scholar
[61]	Wu F C, Lovorn T, Tutuc E, MacDonald A H 2018 Phys. Rev. Lett. 121 026402 Google Scholar
[62]	Koshino M, Yuan N F Q, Koretsune T, Ochi M, Kuroki K, Fu L 2018 Phys. Rev. X 8 031087 Google Scholar
[63]	Wu F C, Lovorn T, Tutuc E, Martin I, MacDonald A H 2019 Phys. Rev. Lett. 122 086402 Google Scholar
[64]	Wang L, Shih E M, Ghiotto A, Xian L D, Rhodes D A, Tan C, Claassen M, Kennes D M, Bai Y S, Kim B, Watanabe K, Taniguchi T, Zhu X Y, Hone J, Rubio A, Pasupathy A N, Dean C R 2020 Nat. Mater. 19 861 Google Scholar
[65]	Tang Y H, Li L Z, Li T X, Xu Y, Liu S, Barmak K, Watanabe K, Taniguchi T, MacDonald A H, Shan J, Mak K F 2020 Nature 579 353 Google Scholar
[66]	Regan E C, Wang D Q, Jin C H, Bakti Utama M I, Gao B N, Wei X, Zhao S H, Zhao W Y, Zhang Z C, Yumigeta K, Blei M, Carlström J D, Watanabe K, Taniguchi T, Tongay S, Crommie M, Zettl A, Wang F 2020 Nature 579 359 Google Scholar
[67]	Huang X, Wang T M, Miao S N, Wang C, Li Z P, Lian Z, Taniguchi T, Watanabe K, Okamoto S, Xiao D, Shi S F, Cui Y T 2021 Nat. Phys. 17 715 Google Scholar
[68]	Jin C H, Tao Z, Li T X, Xu Y, Tang Y H, Zhu J C, Liu S, Watanabe K, Taniguchi T, Hone J C, Fu L, Shan J, Mak K F 2021 Nat. Mater. 20 940 Google Scholar
[69]	Chen J L, Lin X, Chen M Y, Low T, Chen H S, Dai S Y 2021 Appl. Phys. Lett. 119 240501 Google Scholar
[70]	Wu Z L, Liu Y R, Hill E H, Zheng Y B 2018 Nanoscale 10 18096 Google Scholar
[71]	Zhang X Y, Zhong Y H, Low T, Chen H S, Lin X 2021 Phys. Rev. B 103 195405 Google Scholar
[72]	Mao X R, Shao Z K, Luan H Y, Wang S L, Ma R M 2021 Nat. Nanotechnol. 16 1099 Google Scholar
[73]	Jin C H, Regan E C, Yan A M, Iqbal Bakti Utama M, Wang D Q, Zhao S H, Qin Y, Yang S J, Zheng Z R, Shi S Y, Watanabe K, Taniguchi T, Tongay S, Zettl A, Wang F 2019 Nature 567 76 Google Scholar
[74]	Ahn S J, Moon P, Kim T H, Kim H W, Shin H C, Kim E H, Cha H W, Kahng S J, Kim P, Koshino M, Son Y W, Yang C W, Ahn J R 2018 Science 361 782 Google Scholar
[75]	González J, Stauber T 2020 Phys. Rev. Lett. 124 186801 Google Scholar

[1]	陆展鹏, 徐志浩. 具有平带的一维十字型晶格中重返局域化现象. 物理学报, 2024, 73(3): 037202. doi: 10.7498/aps.73.20231393
[2]	刘钊. 莫尔超晶格中的分数化拓扑量子态. 物理学报, 2024, 73(20): 207303. doi: 10.7498/aps.73.20241029
[3]	王继光, 李珑玲, 邱嘉图, 陈许敏, 曹东兴. 钙钛矿超晶格材料界面二维电子气的调控. 物理学报, 2023, 72(17): 176801. doi: 10.7498/aps.72.20230573
[4]	. 二维转角莫尔超晶格专题编者按. 物理学报, 2023, 72(6): 060101. doi: 10.7498/aps.72.060101
[5]	徐琨淇, 胡成, 沈沛约, 马赛群, 周先亮, 梁齐, 史志文. 叠层/转角二维原子晶体结构与极化激元的近场光学表征. 物理学报, 2023, 72(2): 027102. doi: 10.7498/aps.72.20222145
[6]	古杰, 马立国. 莫尔晶格中的激子绝缘体. 物理学报, 2023, 72(6): 067101. doi: 10.7498/aps.72.20230079
[7]	郭瑞平, 俞弘毅. 二维半导体莫尔超晶格中随位置与动量变化的层间耦合. 物理学报, 2023, 72(2): 027302. doi: 10.7498/aps.72.20222046
[8]	吴泽飞, 黄美珍, 王宁. 二维莫尔超晶格中的非线性霍尔效应. 物理学报, 2023, 72(23): 237301. doi: 10.7498/aps.72.20231324
[9]	吴帆帆, 季怡汝, 杨威, 张广宇. 二硫化钼的电子能带结构和低温输运实验进展. 物理学报, 2022, 71(12): 127306. doi: 10.7498/aps.71.20220015
[10]	李听昕. 二维范德瓦耳斯半导体莫尔超晶格实验研究进展. 物理学报, 2022, 71(12): 127309. doi: 10.7498/aps.71.20220347
[11]	詹真, 张亚磊, 袁声军. 石墨烯莫尔超晶格的晶格弛豫与衬底效应. 物理学报, 2022, 71(18): 187302. doi: 10.7498/aps.71.20220872
[12]	张若寒, 任慧莹, 何林. 二维材料平带的实现及其新奇量子物态. 物理学报, 2022, 71(12): 127302. doi: 10.7498/aps.71.20220225
[13]	孙海明. 一维螺旋型Se原子链中的Rashba效应和平带性质. 物理学报, 2022, 71(14): 147102. doi: 10.7498/aps.71.20220646
[14]	夏世强, 唐莉勤, 夏士齐, 马继娜, 燕文超, 宋道红, 胡毅, 许京军, 陈志刚. 平带光子微结构中的新颖现象:从模式局域到实空间拓扑. 物理学报, 2020, 69(15): 154207. doi: 10.7498/aps.69.20200384
[15]	吕新宇, 李志强. 石墨烯莫尔超晶格体系的拓扑性质及光学研究进展. 物理学报, 2019, 68(22): 220303. doi: 10.7498/aps.68.20191317
[16]	卢晓波, 张广宇. 石墨烯莫尔超晶格. 物理学报, 2015, 64(7): 077305. doi: 10.7498/aps.64.077305
[17]	康艳霜, 孙宗利. 荷电流体中静电关联效应的有效势模型. 物理学报, 2014, 63(13): 136101. doi: 10.7498/aps.63.136101
[18]	徐志君, 刘夏吟. 光晶格中非相干超冷原子的密度关联效应. 物理学报, 2011, 60(12): 120305. doi: 10.7498/aps.60.120305
[19]	李宏伟, 王太宏. 含InAs自组装量子点肖特基二极管的关联放电效应. 物理学报, 2001, 50(10): 2038-2043. doi: 10.7498/aps.50.2038
[20]	刘晶南, 孙鑫. 电子关联与二维晶格的不稳定性. 物理学报, 1992, 41(1): 80-86. doi: 10.7498/aps.41.80

计量

文章访问数: 8471
PDF下载量: 740
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

转角二维量子材料中平带相关的新奇电子态物性