Phase transition in bilayer quantum Hall system with opposite magnetic field

doi:10.1088/1674-1056/ace61d

摘要/Abstract

摘要： We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C=±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν_t=1/2+1/2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/l_B is driven. The critical point at d_c/l_B = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/l_B<d_c/l_B, the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r=0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/l_B>d_c/l_B, a crossover from the d→d_c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.

关键词: fractional quantum Hall effect, bilayer quantum Hall system, opposite magnetic field, quantum phase transition

Abstract: We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C=±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν_t=1/2+1/2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/l_B is driven. The critical point at d_c/l_B = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/l_B<d_c/l_B, the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r=0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/l_B>d_c/l_B, a crossover from the d→d_c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.

Key words: fractional quantum Hall effect, bilayer quantum Hall system, opposite magnetic field, quantum phase transition

中图分类号: (Quantum Hall effects)

73.43.-f

73.43.Nq (Quantum phase transitions)

Ke Yang(杨珂). Phase transition in bilayer quantum Hall system with opposite magnetic field[J]. 中国物理B, 2023, 32(9): 97303-097303.

Ke Yang(杨珂). Phase transition in bilayer quantum Hall system with opposite magnetic field[J]. Chin. Phys. B, 2023, 32(9): 97303-097303.

参考文献

[1] Halperin B I and Jain J K 2020 Fractional quantum hall effects: new developments, 1st Ed. (World Scientific)
[2] Niu Q, Thouless D J and Wu Y S 1985 Phys. Rev. B 31 3372
[3] Wen X G 1995 Adv. in Phys. 44 405
[4] Parameswaran S A, Roy R and Sondhi S L 2013 Com. Ren. Phys. 14 816
[5] Neupert T, Santos L, Chamon C and Mudry C 2011 Phys. Rev. Lett. 106 236804
[6] Levin M and Stern A 2009 Phys. Rev. Lett. 103 196803
[7] Eisenstein J P 2014 Annu. Rev. Condens. Matter Phys. 5 159
[8] Eisenstein J P and MacDonald A H 2004 Nature 432 691
[9] Barkeshli M and Wen X G 2011 Phys. Rev. B 84 115121
[10] Suen Y W, Engel L W, Santos M B, Shayegan M and Tsui D C 1992 Phys. Rev. Lett. 68 1376
[11] Luhman D R, Pan W, Tsui D C, Pfeiffer L N, Baldwin K W and West K W 2008 Phys. Rev. Lett. 101 266804
[12] Shabani J, Liu Y, Shayegan M, Pfeiffer L N, West K W and Baldwin K W 2013 Phys. Rev. B 88 245413
[13] Liu Y, Graninger A L, Hasdemir S, Shayegan M, Pfeiffer L N, West K W, Baldwin K W and Winkler R 2014 Phys. Rev. Lett. 112 046804
[14] Peterson M R, Papić Z and Sarma S D 2010 Phys. Rev. B 82 235312
[15] He S, Xie X C, Sarma S D and Zhang F C 1991 Phys. Rev. B 43 9339
[16] Geraedts S, Zaletel M P, Papić Z and Mong R S 2015 Phys. Rev. B 91 205139
[17] Fertig H 1989 Phys. Rev. B 40 1087
[18] Tutuc E, Shayegan M and Huse D A 2004 Phys. Rev. Lett. 93 036802
[19] Wen X G and Zee A 1992 Phys. Rev. Lett. 69 1811
[20] Moon K, Mori H, Yang K, Girvin S M, MacDonald A H, Zheng L, Yoshioka D and Zhang S C 1995 Phys. Rev. B 51 5138
[21] Girvin S M and MacDonald A H 1995 arXiv:cond-mat/9505087v1
[22] Kellogg M, Eisenstein J P, Pfeiffer L N and West K W 2004 Phys. Rev. Lett. 93 036801
[23] Halperin B I 1983 Hel. Phys. Acta 56 75
[24] Halperin B I, Lee P A and Read N 1993 Phys. Rev. B 47 7312
[25] Shibata N and Yoshioka D 2006 J. Phys. Soc. Jpn. 75 043712
[26] Zhu Z, Fu L and Sheng D N 2017 Phys. Rev. Lett. 119 117601
[27] Sheng D N, Balents L and Wang Z Q 2003 Phys. Rev. Lett. 91 116802
[28] Lian B and Zhang S C 2018 Phys. Rev. Lett. 120 077601
[29] Eisenstein J P, Pfeiffer L N and West K W 2019 Phys. Rev. Lett. 123 066802
[30] Liu X M, Li J I A, Watanabe K, Taniguchi T, Hone J, Halperin B I, Kim P and Dean C R 2022 Science 375 205
[31] Moller G, Simon S H and Rezayi E H 2008 Phys. Rev. Lett. 101 176803
[32] Isobe H and Fu L 2017 Phys. Rev. Lett. 118 166401
[33] Wagner G, Nguyen D X, Simon S H and Halperin B I 2021 Phys. Rev. Lett. 127 246803
[34] Scarola V W and Jain J K 2001 Phys. Rev. B 64 085313
[35] Yoshioka D, Macdonald A H and Girvin S M 1989 Phys. Rev. B 39 1932
[36] Read N and Green D 2000 Phys. Rev. B 61 10267
[37] Zhu W, Liu Z, Haldane F D M and Sheng D N 2016 Phys. Rev. B 94 245147
[38] Zhu Z, Sheng D N and Sodemann I 2020 Phys. Rev. Lett. 124 097604
[39] Zhu Z, Sheng D N, Fu L and Sodemann I 2018 Phys. Rev. B 98 155104
[40] Furukawa S and Ueda M 2012 Phys. Rev. A 86 031604
[41] Wu Y H and Jain J K 2013 Phys. Rev. B 87 245123
[42] Wu Y L, Regnault N and Bernevig B A 2013 Phys. Rev. B 110 106802
[43] Sun K, Gu Z C, Katsura H and Sarma S D 2011 Phys. Rev. Lett. 106 236803
[44] Ezawa Z F 2008 Quantum Hall effects: Field theoretical approach, related topics, 2nd Ed. (World Scientific Publishing Company)
[45] Willett R, Eisenstein J P, Stormer H L, Tsui D C, Gossard A C and English J H 1987 Phys. Rev. Lett. 59 1776
[46] Pan W, Stormer H L, Tsui D C, Pfeiffer L N, Baldwin K W and West K W 2003 Phys. Rev. Lett. 90 016801
[47] Mueed M A, Kamburov D, Pfeiffer L N, West K W, Baldwin K W and Shayegan M 2018 arXiv:1810.03600 [cond-mat.str-el]
[57] Schleede J, Filinov A, Bonitz M and Fehske H 2012 Contributions to Plasma Physics 52 819
[58] Boening J, Filinov A and Bonitz M 2011 Phys. Rev. B 84 075130
[59] Astrakharchik G E, Kurbakov I L, Sychev D V, et al. 2021 Phys. Rev. B 103 L140101
[60] Shibata N and Yoshioka D 2004 J. Phys. Soc. Jpn. 73 1
[61] Zhang Y H, Rezayi E H and Yang K 2014 Phys. Rev. B 90 165102
[62] Rezayi E H, Haldane and Yang K 1999 Phys. Rev. Lett. 83 1219
[63] Paquet D, Rice T M and Ueda K 1985 Phys. Rev. B 32 5208
[64] Alicea J, Motrunich and Refael G F 2009 Phys. Rev. Lett. 103 256403
[65] Anderson P W 1984 Phys. Rev. B 30 1549
[66] Randeria M, Duan J M and Shieh L Y 1989 Phys. Rev. Lett. 62 981
[67] Nozieres P and Schmitt-Rink S 1985 J. Low Temp. Phys. 59 195
[68] Chin C, Bartenstein M, Altmeyer A, Riedl S, Jochim S, Hecker Denschlag J and Grimm R 2004 Science 305 5687
[69] Greiner M, Regal C A and Jin D S 2003 Nature 426 537
[70] Zwierlein M W 2014 Superfluidity in ultracold atomic Fermi gases in Novel Superfluids 2 269
[71] Holland M, Kokkelmans, Chiofalo M L and Walser R 2001 Phys. Rev. Lett. 87 120406
[72] Yang K and Zhai H 2008 Phys. Rev. Lett. 100 030404
[73] Chen H and Yang K 2012 Phys. Rev. B 85 195113