Fractionalized topological states in moiré superlattices

Liu Zhao

doi:10.7498/aps.73.20241029

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:

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).

FullText HTML : translate this paragraph

References

[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 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

Cited By

[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 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]	Kun Yang. Geometric degrees of freedom and graviton-like excitations in fractional quantum Hall liquids. Acta Physica Sinica, 2024, 73(17): 177801. doi: 10.7498/aps.73.20240994
[2]	Liu Chang, Wang Ya-Yu. Quantum transport phenomena in magnetic topological insulators. Acta Physica Sinica, 2023, 72(17): 177301. doi: 10.7498/aps.72.20230690
[3]	Zhang Shuai, Song Feng-Qi. Research progress of quantum Hall effect in topological insulator. Acta Physica Sinica, 2023, 72(17): 177302. doi: 10.7498/aps.72.20230698
[4]	Gu Jie, Ma Li-Guo. Exciton insulator in a moiré lattice. Acta Physica Sinica, 2023, 72(6): 067101. doi: 10.7498/aps.72.20230079
[5]	Xu Kun-Qi, Hu Cheng, Shen Pei-Yue, Ma Sai-Qun, Zhou Xian-Liang, Liang Qi, Shi Zhi-Wen. Near-field optical characterization of atomic structures and polaritons in twisted two-dimensional materials. Acta Physica Sinica, 2023, 72(2): 027102. doi: 10.7498/aps.72.20222145
[6]	Guo Rui-Ping, Yu Hong-Yi. Position- and momentum-dependent interlayer couplings in two-dimensional semiconductor moiré superlattices. Acta Physica Sinica, 2023, 72(2): 027302. doi: 10.7498/aps.72.20222046
[7]	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
[8]	Li Qing-Xin, Huang Yan, Chen Yi-Wei, Zhu Yu-Jian, Zhu Wang, Song Jun-Wei, An Dong-Dong, Gan Qi-Kang, Wang Kai-Yuan, Wang Hao-Lin, Mai Zhi-Hong, Xi Chuan-Ying, Zhang Jing-Lei, Yu Ge-Liang, Wang Lei. Even-denominator fractional quantum Hall state in bilayer graphene. Acta Physica Sinica, 2022, 71(18): 187202. doi: 10.7498/aps.71.20220905
[9]	Wu Fan-Fan, Ji Yi-Ru, Yang Wei, Zhang Guang-Yu. Experimental research progress of electronic band structure and low temperature transport based on molybdenum disulfide. Acta Physica Sinica, 2022, 71(12): 127306. doi: 10.7498/aps.71.20220015
[10]	Wang Zhong-Rui, Jiang Yu-Hang. Physical properties of novel electronic states related to flat band in twisted two-dimensional quantum materials. Acta Physica Sinica, 2022, 71(12): 127202. doi: 10.7498/aps.71.20220064
[11]	Li Ting-Xin. Recent experimental research progress of two-dimensional van der Waals semiconductor moiré superlattices. Acta Physica Sinica, 2022, 71(12): 127309. doi: 10.7498/aps.71.20220347
[12]	Zhan Zhen, Zhang Ya-Lei, Yuan Sheng-Jun. Lattice relaxation and substrate effects of graphene moiré superlattice. Acta Physica Sinica, 2022, 71(18): 187302. doi: 10.7498/aps.71.20220872
[13]	Wang Hang-Tian, Zhao Hai-Hui, Wen Liang-Gong, Wu Xiao-Jun, Nie Tian-Xiao, Zhao Wei-Sheng. High-performance THz emission: From topological insulator to topological spintronics. Acta Physica Sinica, 2020, 69(20): 200704. doi: 10.7498/aps.69.20200680
[14]	He Ying-Ping, Hong Jian-Song, Liu Xiong-Jun. Non-abelian statistics of Majorana modes and the applications to topological quantum computation. Acta Physica Sinica, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
[15]	Jia Ding, Ge Yong, Yuan Shou-Qi, Sun Hong-Xiang. Dual-band acoustic topological insulator based on honeycomb lattice sonic crystal. Acta Physica Sinica, 2019, 68(22): 224301. doi: 10.7498/aps.68.20190951
[16]	Xiang Tian, Cheng Liang, Qi Jing-Bo. Ultrafast charge and spin dynamics on topological insulators. Acta Physica Sinica, 2019, 68(22): 227202. doi: 10.7498/aps.68.20191433
[17]	Lü Xin-Yu, Li Zhi-Qiang. Topological properties of graphene moiré superlattice systems and recent optical studies. Acta Physica Sinica, 2019, 68(22): 220303. doi: 10.7498/aps.68.20191317
[18]	Lu Xiao-Bo, Zhang Guang-Yu. Graphene/h-BN Moiré superlattice. Acta Physica Sinica, 2015, 64(7): 077305. doi: 10.7498/aps.64.077305
[19]	XIONG XIAO-MING, ZHOU SHI-XUN. EIGENENERGIES OF THE FRACTIONAL QUANTUM HALL EFFECT SYSTEM IN THE MASS CENTRE COORDINATE. Acta Physica Sinica, 1988, 37(6): 1010-1013. doi: 10.7498/aps.37.1010
[20]	XIONG XIAO-MING, ZHOU SHI-XUN. FINITE CLUSTER STUDIES OF THE FQHE. Acta Physica Sinica, 1987, 36(12): 1630-1634. doi: 10.7498/aps.36.1630

Catalog

Vol. 73, Issue 20 - 2024-10-20

Metrics

Abstract views: 842
PDF Downloads: 72
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