Please wait a minute...
Chin. Phys. B, 2019, Vol. 28(6): 067303    DOI: 10.1088/1674-1056/28/6/067303
RAPID COMMUNICATION Prev   Next  

Neutral excitation and bulk gap of fractional quantum Hall liquids in disk geometry

Wu-Qing Yang(杨武庆)1, Qi Li(李骐)2,3, Lin-Peng Yang(杨林鹏)1, Zi-Xiang Hu(胡自翔)1
1 Department of Physics, Chongqing University, Chongqing 401331, China;
2 Department of Physics, South University of Science and Technology of China, Shenzhen 518055, China;
3 School of Physics and Technology, Wuhan University, Wuhan 430072, China
Abstract  

For the numerical simulation of the fractional quantum Hall (FQH) effects on a finite disk, the rotational symmetry is the only symmetry that is used in diagonalizing the Hamiltonian. In this work, we propose a method of using the weak translational symmetry for the center of mass of the many-body system. With this approach, the bulk properties, such as the energy gap and the magneto-roton excitation are consistent with those in the closed manifolds like the sphere and torus. As an application, we consider the FQH phase and its phase transition in the fast rotated dipolar fermions. We thus demonstrate the disk geometry having versatility in analyzing the bulk properties beside the usual edge physics.

Keywords:  fractional quantum Hall      bulk states      edge states      magneto-roton      dipolar-dipolar interaction  
Received:  22 March 2019      Revised:  04 April 2019      Accepted manuscript online: 
PACS:  73.43.Lp (Collective excitations)  
  71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 11674041, 91630205, 11474144, and 11847301), Chongqing Research Program of Basic Research and Frontier Technology (Grant No. cstc2017jcyjAX0084), and FRF for the Central Universities (Grant No. 2019CDJDWL0005).

Corresponding Authors:  Zi-Xiang Hu     E-mail:  zxhu@cqu.edu.cn

Cite this article: 

Wu-Qing Yang(杨武庆), Qi Li(李骐), Lin-Peng Yang(杨林鹏), Zi-Xiang Hu(胡自翔) Neutral excitation and bulk gap of fractional quantum Hall liquids in disk geometry 2019 Chin. Phys. B 28 067303

[1] Tsui D C, Störmer H L and Gossard A C 1982 Phys. Rev. Lett. 48 1559
[2] Shibata N and Yoshioka D 2001 Phys. Rev. Lett. 86 5755
[3] Feiguin A E, Rezayi E, Nayak C and Das Sarma S 2008 Phys. Rev. Lett. 100 166803
[4] Zhao J Z, Sheng D N, Haldane F D M 2011 Phys. Rev. B 83 195135
[5] Hu Z X, Papic Z, Johri S, Bhatt R N and Schmitteckert P 2012 Phys. Lett. A 376 2157
[6] Zaletel M P, Mong R S K, and Pollmann F 2013 Phys. Rev. Lett. 110 236801
[7] Girvin S M, MacDonald A H and Platzman P M 1985 Phys. Rev. Lett. 54 581
[8] Girvin S M, MacDonald A H and Platzman P M 1986 Phys. Rev. B 33 2481
[9] Yang B, Hu Z X, Papic Z and Haldane F D M 2012 Phys. Rev. Lett. 108 256807
[10] Wen X G 1992 Int. J. Mod. Phys. B 6 1711
[11] Kan C L and Fisher M P A 1992 Phys. Rev. B 46 15233
[12] Moon K, Yi H, Kane C L, Girvin S M and Fisher M P A 1993 Phys. Rev. Lett. 71 4381
[13] Kane C L and Fisher M P A 1994 Phys. Rev. Lett. 72 724
[14] Chamon C de C and Wen X G 1993 Phys. Rev. Lett. 70 2605
[15] Lin X, Dillard C, Kastner M A, Pfeiffer L N and West K W 2012 Phys. Rev. B 85 165321
[16] Li Q, Jiang N, Wan X and Hu Z X 2018 J. Phys.: Condens. Matter 30 255601
[17] Hu Z X, Lee K H, Rezayi E H, Wan X and Yang K 2011 New J. Phys. 13 035020
[18] Fendley P, Fisher M P A and Nayak C 2007 Phys. Rev. B 75 045317
[19] Fradkin E, Nayak C, Tsvelik A and Wilczek F 1998 Nucl. Phys. B 516 704
[20] Das Sarma S, Freedman M and Nayak C 2005 Phys. Rev. Lett. 94 166802
[21] Stern A and Halperin B I 2006 Phys. Rev. Lett. 96 016802
[22] Rosenow B, Halperin B I, Simon S H and Stern A 2008 Phys. Rev. Lett. 100 226803
[23] Bishara B and Nayak C 2008 Phys. Rev. B 77 165302
[24] Bonderson P, Shtengel K and Slingerland J K 2006 Phys. Rev. Lett. 97 016401
[25] Willett R L, Pfeiffer L N and West K W 2009 Proc. Natl, Acad. Sci. 106 8853
[26] Willett R L, Pfeiffer L N and West K W 2010 Phys. Rev. B 82 205301
[27] Willett R L, Pfeiffer L N and West K W 2013 arXiv: 1301.2594
[28] Lin X, Du R R and Xie X C 2014 National Science Review 1 564
[29] MacDonald A H 1990 Phys. Rev. Lett. 64 220
[30] Chamon C de C and Wen X G 1994 Phys. Rev. B 49 8227
[31] Wan X, Rezayi E H and Yang K 2003 Phys. Rev. B 68 125307
[32] Wang J H, Meir Y and Gefen Y 2013 Phys. Rev. Lett. 111 246803
[33] Sabo R, Gurman I, et al. 2017 Nat. Phys. 13 491
[34] Li H, Haldane F D M 2008 Phys. Rev. Lett. 101 010504
[35] Laughlin R B 1981 Phys. Rev. B 23 5632
[36] Dolgopolov V T, Shashkin A A, Zhitenev N B, Dorozhkin S I and Klitzing K von 1992 Phys. Rev. B 46 12560
[37] Zhu Z Y, Wang P J, Fu H L, Pfeiffer L N, West K W, Du R R and Lin X 2018 Physica E 95 1
[38] Cooper N R 2008 Adv. Phys. 57 539
[39] Haldane F D M 1983 Phys. Rev. Lett. 51 605
[40] Laughlin R B 1983 Phys. Rev. Lett. 50 1395
[41] Hu Z X, Wan X and Schmitteckert P 2008 Phys. Rev. B 77 075331
[42] Griesmaier A, Werner J, Hensler S, Stuhler J and Pfau T 2005 Phys. Rev. Lett. 94 160401
[43] Myatt C J, Burt E A, Ghrist R W, Cornell E A and Wieman E A 1997 Phys. Rev. Lett. 78 586
[44] Fetter A L 2009 Rev. Mod. Phys. 81 647
[45] Baranov M A, Osterloh K and Lewenstein M 2005 Phys. Rev. Lett. 94 070404
[46] Osterloh K, Barberán N, and Lewenstein M 2007 Phys. Rev. Lett. 99 160403
[47] Baranov M A, Fehrmann H, and Lewenstein M 2008 Phys. Rev. Lett. 100 200402
[48] Yang B, Hu Z X, Lee C H and Papic Z 2017 Phys. Rev. Lett. 118 146403
[49] Yang L P, Li Q and Hu Z X 2018 Chin. Phys. B 27 087306
[50] Hu Z X, Li Q, Yang L P, Yang W Q, Jiang N, Qiu R Z and Yang B 2018 Phys. Rev. B 97 035140
[51] Qiu R Z, Kou S P, Hu Z X, Wan X and Yi S 2011 Phys. Rev. A 83 063633
[52] Haldane F D M 2011 Phys. Rev. Lett. 107 116801
[53] Qiu R Z, Haldane F D M, Wan X, Yang K and Yi S 2012 Phys. Rev. B 85 115308
[54] Yang B, Papic Z, Rezayi E H, Bhatt R N and Haldane F D M 2012 Phys. Rev. B 85 165318
[1] Floquet bands and photon-induced topological edge states of graphene nanoribbons
Weijie Wang(王威杰), Xiaolong Lü(吕小龙), and Hang Xie(谢航). Chin. Phys. B, 2021, 30(6): 066701.
[2] Quantum dynamics on a lossy non-Hermitian lattice
Li Wang(王利), Qing Liu(刘青), and Yunbo Zhang(张云波). Chin. Phys. B, 2021, 30(2): 020506.
[3] Evidence for topological superconductivity: Topological edge states in Bi2Te3/FeTe heterostructure
Bin Guo(郭斌), Kai-Ge Shi(师凯歌), Hai-Lang Qin(秦海浪), Liang Zhou(周良), Wei-Qiang Chen(陈伟强), Fei Ye(叶飞), Jia-Wei Mei(梅佳伟), Hong-Tao He(何洪涛), Tian-Luo Pan(潘天洛), Gan Wang(王干). Chin. Phys. B, 2020, 29(9): 097403.
[4] Symmetry-controlled edge states in graphene-like topological sonic crystal
Zhang-Zhao Yang(杨彰昭), Jin-Heng Chen(陈晋恒), Yao-Yin Peng(彭尧吟), and Xin-Ye Zou(邹欣晔)†. Chin. Phys. B, 2020, 29(10): 104302.
[5] Ground-state vortex structures of a rotating binary dipolar Bose-Einstein condensate confined in harmonic plus quartic potential
Guang-Ping Chen(陈光平), Chang-Bing Qiao(乔昌兵), Hui Guo(郭慧), Lin-Xue Wang(王林雪), Ya-Jun Wang(王雅君), Ren-Bing Tan(谭仁兵). Chin. Phys. B, 2019, 28(1): 010308.
[6] Behavior of fractional quantum Hall states in LLL and 1LL with in-plane magnetic field and Landau level mixing: A numerical investigation
Lin-Peng Yang(杨林鹏), Qi Li(李骐), Zi-Xiang Hu(胡自翔). Chin. Phys. B, 2018, 27(8): 087306.
[7] Sub-millikelvin station at Synergetic Extreme Condition User Facility
Zhi Gang Cheng(程智刚), Jie Fan(樊洁), Xiunian Jing(景秀年), Li Lu(吕力). Chin. Phys. B, 2018, 27(7): 070702.
[8] Topological edge states and electronic structures of a 2D topological insulator: Single-bilayer Bi (111)
Gao Chun-Lei, Qian Dong, Liu Can-Hua, Jia Jin-Feng, Liu Feng. Chin. Phys. B, 2013, 22(6): 067304.
No Suggested Reading articles found!