莫尔超晶格中的分数化拓扑量子态

刘钊

doi:10.7498/aps.73.20241029

摘要

带有分数化准粒子激发的分数量子霍尔态是一种奇特的强关联拓扑量子物态, 自1982年在强磁场二维电子气中被首次观测到以来一直是凝聚态物理重要的前沿方向. 去年来, 有多个团队在基于过渡金属硫族化合物和石墨烯的莫尔超晶格中观测到了零磁场分数量子霍尔效应, 在莫尔超晶格中还发现了分数量子自旋霍尔效应的迹象. 这表明莫尔超晶格体系能够有效调控能带及相互作用, 是在零磁场条件下实现分数化拓扑量子态的理想平台. 本文简要论述了与此相关的研究进展和存在的挑战, 并对该领域未来可能的发展方向做出展望.

关键词:

Abstract

Fractional quantum Hall (FQH) states with fractionalized quasiparticles are exotic topologically ordered quantum states driven by strong correlation between particles. Since the first discovery in 1982 in two-dimensional electron gases penetrated by strong magnetic fields, FQH physics has become an attractive frontier of condensed matter physics. Since last year, FQH transport at zero magnetic field has been observed in moiré superlattices based on transition metal dichalcogenides (TMDs) and graphene. Furthermore, the evidence of fractional quantum spin Hall effect has also been reported in TMD moiré superlattices. These results demonstrate that moiré superlattices are an ideal platform for controlling band structures and interactions to realize fractionalized topological states without the intervention of external magnetic fields. In this paper, we will briefly review the recent research progress on fractionalized topological states in moiré superlattices, summarize the existing challenges, and discuss possible future development of this field.

Keywords:

作者及机构信息

刘钊

浙江大学物理学院, 浙江近代物理中心, 杭州　310058

通信作者: 刘钊, zhaol@zju.edu.cn

基金项目: 国家自然科学基金(批准号: 12374149, 12350403)资助的课题.

Authors and contacts

Liu Zhao

Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China

Corresponding author: Liu Zhao, zhaol@zju.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12374149, 12350403).

文章全文 : translate this paragraph

参考文献

[1]	Kang K, Shen B, Qiu Y, Zeng Y, Xia Z, Watanabe K, Taniguchi T, Shan J, Mak K F 2024 Nature 628 522 Google Scholar
[2]	Moore G, Read N 1991 Nucl. Phys. B 360 362 Google Scholar
[3]	Cai J, Anderson E, Wang C, Zhang X, Liu X, Holtzmann W, Zhang Y, Fan F, Taniguchi T, Watanabe K, Ran Y, Cao T, Fu L, Xiao D, Yao W, Xu X 2023 Nature 622 63 Google Scholar
[4]	Zeng Y, Xia Z, Kang K, Zhu J, Knüppel P, Vaswani C, Watanabe K, Taniguchi T, Mak K F, Shan J 2023 Nature 622 69 Google Scholar
[5]	Park H, Cai J, Anderson E, Zhang Y, Zhu J, Liu X, Wang C, Holtzmann W, Hu C, Liu Z, Taniguchi T, Watanabe K, Chu J H, Cao T, Fu L, Yao W, Chang C Z, Cobden D, Xiao D, Xu X 2023 Nature 622 74 Google Scholar
[6]	Xu F, Sun Z, Jia T, Liu C, Xu C, Li C, Gu Y, Watanabe K, Taniguchi T, Tong B, Jia J, Shi Z, Jiang S, Zhang Y, Liu X, Li T 2023 Phys. Rev. X 13 031037 Google Scholar
[7]	Lu Z, Han T, Yao Y, Reddy A P, Yang J, Seo J, Watanabe K, Taniguchi T, Fu L, Ju L 2024 Nature 626 759 Google Scholar
[8]	Xie J, Huo Z, Lu X, Feng Z, Zhang Z, Wang W, Yang Q, Watanabe K, Taniguchi T, Liu K, Song Z, Xie X C, Liu J, Lu X 2024 arXiv 2405.16944
[9]	Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[10]	Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559 Google Scholar
[11]	Wen X G 1995 Adv. Phys. 44 405 Google Scholar
[12]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[13]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[14]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, 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
[15]	Tang E, Mei J W, Wen X G 2011 Phys. Rev. Lett. 106 236802 Google Scholar
[16]	Sun K, Gu Z, Katsura H, Sarma S D 2011 Phys. Rev. Lett. 106 236803 Google Scholar
[17]	Neupert T, Santos L, Chamon C, Mudry C 2011 Phys. Rev. Lett. 106 236804 Google Scholar
[18]	Sheng D N, Gu Z C, Sun K, Sheng L 2011 Nat. Commun. 2 389 Google Scholar
[19]	Regnault N, Bernevig B A 2011 Phys. Rev. X 1 021014 Google Scholar
[20]	Parameswaran S A, Roy R, Sondhi S L 2013 C.R. Phys. 14 816 Google Scholar
[21]	Bergholtz E J, Liu Z 2013 Int. J. Mod. Phys. B 27 1330017 Google Scholar
[22]	Neupert T, Chamon C, Iadecola T, Santos L H, Mudry C 2015 Phys. Scr. 2015 014005 Google Scholar
[23]	杨威 2023 物理学报 72 060101 Google Scholar Yang W 2023 Acta Phys. Sin. 72 060101 Google Scholar
[24]	Abouelkomsan A, Liu Z, Bergholtz E J 2020 Phys. Rev. Lett. 124 106803 Google Scholar
[25]	Repellin C, Senthil T 2020 Phys. Rev. Research 2 023238 Google Scholar
[26]	Ledwith P J, Tarnopolsky G, Khalaf E, Vishwanath A 2020 Phys. Rev. Research 2 023237 Google Scholar
[27]	Liu Z, Abouelkomsan A, Bergholtz E J 2021 Phys. Rev. Lett. 126 026801 Google Scholar
[28]	Crepel V, Fu L 2023 Phys. Rev. B 107 L201109 Google Scholar
[29]	Li H, Kumar U, Sun K, Lin S Z 2021 Phys. Rev. Research 3 L032070 Google Scholar
[30]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[31]	Bernevig B A, Zhang S C 2006 Phys. Rev. Lett. 96 106802 Google Scholar
[32]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[33]	Wang C, Zhang X W, Liu X, Wang J, Cao T, Xiao D 2024 arXiv 2404.05697
[34]	Reddy A P, Paul N, Abouelkomsan A, Fu L 2024 arXiv 2403.00059
[35]	Ahn C E, Lee W, Yananose K, Kim Y, Cho G Y 2024 arXiv 2403.19155
[36]	Abouelkomsan A, Fu L 2024 arXiv 2406.14617
[37]	Sodemann Villadiego I 2024 Phys. Rev. B 110 045114 Google Scholar
[38]	Zhang Y H 2024 arXiv 2402.05112
[39]	Jian C M, Cheng M, Xu C 2024 arXiv 2403.07054
[40]	May-Mann J, Stern A, Devakul T 2024 arXiv 2403.03964
[41]	Zhang Y H 2024 arXiv 2403.12126
[42]	Wang C, Zhang X W, Liu X, He Y, Xu X, Ran Y, Cao T, Xiao D 2024 Phys. Rev. Lett. 132 036501 Google Scholar
[43]	Reddy A P, Alsallom F, Zhang Y, Devakul T, Fu L 2023 Phys. Rev. B 108 085117 Google Scholar
[44]	Yu J, Herzog-Arbeitman H, Wang M, Vafek O, Andrei Bernevig B, Regnault N 2024 Phys. Rev. B 109 045147 Google Scholar
[45]	Xu C, Li J, Xu Y, Zhang Y 2024 PNAS 121 e2316749121 Google Scholar
[46]	Herzog-Arbeitman J, Wang Y, Liu J, Tam P M, Qi Z, Jia Y, Efetov D K, Vafek O, Regnault N, Weng H, Wu Q, Bernevig B A, Yu J 2024 Phys. Rev. B 109 205122 Google Scholar
[47]	Dong Z, Patri A S, Senthil T 2023 arXiv 2311.03445
[48]	Zhou B, Yang H, Zhang Y H 2024 arXiv 2311.04217
[49]	Dong J, Wang T, Wang T, Soejima T, Zaletel M P, Vishwanath A, Parker D E 2024 arXiv 2311.05568
[50]	Guo Z, Lu X, Xie B, Liu J 2023 Phys. Rev. B 110 075109
[51]	Kwan Y H, Yu J, Herzog-Arbeitman J, Efetov D K, Regnault N, Bernevig B A 2023 arXiv 2312.11617
[52]	Lu Z, Han T, Yao Y, Yang J, Seo J, Shi L, Ye S, Watanabe K, Taniguchi T, Ju L 2024 arXiv 2408.10203
[53]	Waters D, Okounkova A, Su R, Zhou B, Yao J, Watanabe K, Taniguchi T, Xu X, Zhang Y H, Folk J, Yankowitz M 2024 arXiv 2408.10133
[54]	Yu J, Herzog-Arbeitman J, Kwan Y H, Regnault N, Bernevig B A 2024 arXiv 2407.13770
[55]	Ji Z, Park H, Barber M E, Hu C, Watanabe K, Taniguchi T, Chu J H, Xu X, Shen Z X 2024 arXiv 2404.07157
[56]	Park H, Cai J, Anderson E, Zhang X W, Liu X, Holtzmann W, Li W, Wang C, Hu C, Zhao Y, Taniguchi T, Watanabe K, Yang J, Cobden D, Chu J H, Regnault N, Bernevig B A, Fu L, Cao T, Xiao D, Xu X 2024 arXiv 2406.09591
[57]	Xu F, Chang X, Xiao J, Zhang Y, Liu F, Sun Z, Mao N, Peshcherenko N, Li J, Watanabe K, Taniguchi T, Tong B, Lu L, Jia J, Qian D, Shi Z, Zhang Y, Liu X, Jiang S, Li T 2024 arXiv 2406.09687
[58]	Kwan Y H, Wagner G, Yu J, Dagnino A K, Jiang Y, Xu X, Bernevig B A, Neupert T, Regnault N 2024 arXiv 2407.02560

施引文献

[1]	Kang K, Shen B, Qiu Y, Zeng Y, Xia Z, Watanabe K, Taniguchi T, Shan J, Mak K F 2024 Nature 628 522 Google Scholar
[2]	Moore G, Read N 1991 Nucl. Phys. B 360 362 Google Scholar
[3]	Cai J, Anderson E, Wang C, Zhang X, Liu X, Holtzmann W, Zhang Y, Fan F, Taniguchi T, Watanabe K, Ran Y, Cao T, Fu L, Xiao D, Yao W, Xu X 2023 Nature 622 63 Google Scholar
[4]	Zeng Y, Xia Z, Kang K, Zhu J, Knüppel P, Vaswani C, Watanabe K, Taniguchi T, Mak K F, Shan J 2023 Nature 622 69 Google Scholar
[5]	Park H, Cai J, Anderson E, Zhang Y, Zhu J, Liu X, Wang C, Holtzmann W, Hu C, Liu Z, Taniguchi T, Watanabe K, Chu J H, Cao T, Fu L, Yao W, Chang C Z, Cobden D, Xiao D, Xu X 2023 Nature 622 74 Google Scholar
[6]	Xu F, Sun Z, Jia T, Liu C, Xu C, Li C, Gu Y, Watanabe K, Taniguchi T, Tong B, Jia J, Shi Z, Jiang S, Zhang Y, Liu X, Li T 2023 Phys. Rev. X 13 031037 Google Scholar
[7]	Lu Z, Han T, Yao Y, Reddy A P, Yang J, Seo J, Watanabe K, Taniguchi T, Fu L, Ju L 2024 Nature 626 759 Google Scholar
[8]	Xie J, Huo Z, Lu X, Feng Z, Zhang Z, Wang W, Yang Q, Watanabe K, Taniguchi T, Liu K, Song Z, Xie X C, Liu J, Lu X 2024 arXiv 2405.16944
[9]	Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[10]	Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559 Google Scholar
[11]	Wen X G 1995 Adv. Phys. 44 405 Google Scholar
[12]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[13]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[14]	Chang C Z, Zhang J, Feng X, Shen J, Zhang Z, Guo M, Li K, Ou Y, Wei P, Wang L L, Ji Z Q, 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
[15]	Tang E, Mei J W, Wen X G 2011 Phys. Rev. Lett. 106 236802 Google Scholar
[16]	Sun K, Gu Z, Katsura H, Sarma S D 2011 Phys. Rev. Lett. 106 236803 Google Scholar
[17]	Neupert T, Santos L, Chamon C, Mudry C 2011 Phys. Rev. Lett. 106 236804 Google Scholar
[18]	Sheng D N, Gu Z C, Sun K, Sheng L 2011 Nat. Commun. 2 389 Google Scholar
[19]	Regnault N, Bernevig B A 2011 Phys. Rev. X 1 021014 Google Scholar
[20]	Parameswaran S A, Roy R, Sondhi S L 2013 C.R. Phys. 14 816 Google Scholar
[21]	Bergholtz E J, Liu Z 2013 Int. J. Mod. Phys. B 27 1330017 Google Scholar
[22]	Neupert T, Chamon C, Iadecola T, Santos L H, Mudry C 2015 Phys. Scr. 2015 014005 Google Scholar
[23]	杨威 2023 物理学报 72 060101 Google Scholar Yang W 2023 Acta Phys. Sin. 72 060101 Google Scholar
[24]	Abouelkomsan A, Liu Z, Bergholtz E J 2020 Phys. Rev. Lett. 124 106803 Google Scholar
[25]	Repellin C, Senthil T 2020 Phys. Rev. Research 2 023238 Google Scholar
[26]	Ledwith P J, Tarnopolsky G, Khalaf E, Vishwanath A 2020 Phys. Rev. Research 2 023237 Google Scholar
[27]	Liu Z, Abouelkomsan A, Bergholtz E J 2021 Phys. Rev. Lett. 126 026801 Google Scholar
[28]	Crepel V, Fu L 2023 Phys. Rev. B 107 L201109 Google Scholar
[29]	Li H, Kumar U, Sun K, Lin S Z 2021 Phys. Rev. Research 3 L032070 Google Scholar
[30]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[31]	Bernevig B A, Zhang S C 2006 Phys. Rev. Lett. 96 106802 Google Scholar
[32]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[33]	Wang C, Zhang X W, Liu X, Wang J, Cao T, Xiao D 2024 arXiv 2404.05697
[34]	Reddy A P, Paul N, Abouelkomsan A, Fu L 2024 arXiv 2403.00059
[35]	Ahn C E, Lee W, Yananose K, Kim Y, Cho G Y 2024 arXiv 2403.19155
[36]	Abouelkomsan A, Fu L 2024 arXiv 2406.14617
[37]	Sodemann Villadiego I 2024 Phys. Rev. B 110 045114 Google Scholar
[38]	Zhang Y H 2024 arXiv 2402.05112
[39]	Jian C M, Cheng M, Xu C 2024 arXiv 2403.07054
[40]	May-Mann J, Stern A, Devakul T 2024 arXiv 2403.03964
[41]	Zhang Y H 2024 arXiv 2403.12126
[42]	Wang C, Zhang X W, Liu X, He Y, Xu X, Ran Y, Cao T, Xiao D 2024 Phys. Rev. Lett. 132 036501 Google Scholar
[43]	Reddy A P, Alsallom F, Zhang Y, Devakul T, Fu L 2023 Phys. Rev. B 108 085117 Google Scholar
[44]	Yu J, Herzog-Arbeitman H, Wang M, Vafek O, Andrei Bernevig B, Regnault N 2024 Phys. Rev. B 109 045147 Google Scholar
[45]	Xu C, Li J, Xu Y, Zhang Y 2024 PNAS 121 e2316749121 Google Scholar
[46]	Herzog-Arbeitman J, Wang Y, Liu J, Tam P M, Qi Z, Jia Y, Efetov D K, Vafek O, Regnault N, Weng H, Wu Q, Bernevig B A, Yu J 2024 Phys. Rev. B 109 205122 Google Scholar
[47]	Dong Z, Patri A S, Senthil T 2023 arXiv 2311.03445
[48]	Zhou B, Yang H, Zhang Y H 2024 arXiv 2311.04217
[49]	Dong J, Wang T, Wang T, Soejima T, Zaletel M P, Vishwanath A, Parker D E 2024 arXiv 2311.05568
[50]	Guo Z, Lu X, Xie B, Liu J 2023 Phys. Rev. B 110 075109
[51]	Kwan Y H, Yu J, Herzog-Arbeitman J, Efetov D K, Regnault N, Bernevig B A 2023 arXiv 2312.11617
[52]	Lu Z, Han T, Yao Y, Yang J, Seo J, Shi L, Ye S, Watanabe K, Taniguchi T, Ju L 2024 arXiv 2408.10203
[53]	Waters D, Okounkova A, Su R, Zhou B, Yao J, Watanabe K, Taniguchi T, Xu X, Zhang Y H, Folk J, Yankowitz M 2024 arXiv 2408.10133
[54]	Yu J, Herzog-Arbeitman J, Kwan Y H, Regnault N, Bernevig B A 2024 arXiv 2407.13770
[55]	Ji Z, Park H, Barber M E, Hu C, Watanabe K, Taniguchi T, Chu J H, Xu X, Shen Z X 2024 arXiv 2404.07157
[56]	Park H, Cai J, Anderson E, Zhang X W, Liu X, Holtzmann W, Li W, Wang C, Hu C, Zhao Y, Taniguchi T, Watanabe K, Yang J, Cobden D, Chu J H, Regnault N, Bernevig B A, Fu L, Cao T, Xiao D, Xu X 2024 arXiv 2406.09591
[57]	Xu F, Chang X, Xiao J, Zhang Y, Liu F, Sun Z, Mao N, Peshcherenko N, Li J, Watanabe K, Taniguchi T, Tong B, Lu L, Jia J, Qian D, Shi Z, Zhang Y, Liu X, Jiang S, Li T 2024 arXiv 2406.09687
[58]	Kwan Y H, Wagner G, Yu J, Dagnino A K, Jiang Y, Xu X, Bernevig B A, Neupert T, Regnault N 2024 arXiv 2407.02560

[1]	杨昆. 分数量子霍尔液体中的几何自由度及类引力子元激发. 物理学报, 2024, 73(17): 177801. doi: 10.7498/aps.73.20240994
[2]	刘畅, 王亚愚. 磁性拓扑绝缘体中的量子输运现象. 物理学报, 2023, 72(17): 177301. doi: 10.7498/aps.72.20230690
[3]	张帅, 宋凤麒. 拓扑绝缘体中量子霍尔效应的研究进展. 物理学报, 2023, 72(17): 177302. doi: 10.7498/aps.72.20230698
[4]	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
[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]	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
[7]	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
[8]	李庆鑫, 黄焱, 陈以威, 朱雨剑, 朱旺, 宋珺威, 安冬冬, 甘祺康, 王开元, 王浩林, 麦志洪, Andy Shen, 郗传英, 张警蕾, 于葛亮, 王雷. 双层石墨烯中的偶数分母分数量子霍尔态. 物理学报, 2022, 71(18): 187202. doi: 10.7498/aps.71.20220905
[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]	王仲锐, 姜宇航. 转角二维量子材料中平带相关的新奇电子态物性. 物理学报, 2022, 71(12): 127202. doi: 10.7498/aps.71.20220064
[11]	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
[12]	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
[13]	王航天, 赵海慧, 温良恭, 吴晓君, 聂天晓, 赵巍胜. 高性能太赫兹发射: 从拓扑绝缘体到拓扑自旋电子. 物理学报, 2020, 69(20): 200704. doi: 10.7498/aps.69.20200680
[14]	何映萍, 洪健松, 刘雄军. 马约拉纳零能模的非阿贝尔统计及其在拓扑量子计算的应用. 物理学报, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
[15]	贾鼎, 葛勇, 袁寿其, 孙宏祥. 基于蜂窝晶格声子晶体的双频带声拓扑绝缘体. 物理学报, 2019, 68(22): 224301. doi: 10.7498/aps.68.20190951
[16]	向天, 程亮, 齐静波. 拓扑绝缘体中的超快电荷自旋动力学. 物理学报, 2019, 68(22): 227202. doi: 10.7498/aps.68.20191433
[17]	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
[18]	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
[19]	熊小明, 周世勋. 质心坐标系中分数量子Hall效应体系的能量本征值. 物理学报, 1988, 37(6): 1010-1013. doi: 10.7498/aps.37.1010
[20]	熊小明, 周世勋. 分数量子Hall效应的有限集团研究. 物理学报, 1987, 36(12): 1630-1634. doi: 10.7498/aps.36.1630

计量

文章访问数: 1067
PDF下载量: 87
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