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 νt=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/lB is driven. The critical point at dc/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB<dc/lB, 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/lB>dc/lB, a crossover from the d→dc 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.
Corresponding Authors:
Ke Yang
E-mail: yangke@ucas.ac.cn
Cite this article:
Ke Yang(杨珂) Phase transition in bilayer quantum Hall system with opposite magnetic field 2023 Chin. Phys. B 32 097303
[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. B31 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 Nature432 691 [9] Barkeshli M and Wen X G 2011 Phys. Rev. B84 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. B88 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. B82 235312 [15] He S, Xie X C, Sarma S D and Zhang F C 1991 Phys. Rev. B43 9339 [16] Geraedts S, Zaletel M P, Papić Z and Mong R S 2015 Phys. Rev. B91 205139 [17] Fertig H 1989 Phys. Rev. B40 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. B51 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. Acta56 75 [24] Halperin B I, Lee P A and Read N 1993 Phys. Rev. B47 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 Science375 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. B64 085313 [35] Yoshioka D, Macdonald A H and Girvin S M 1989 Phys. Rev. B39 1932 [36] Read N and Green D 2000 Phys. Rev. B61 10267 [37] Zhu W, Liu Z, Haldane F D M and Sheng D N 2016 Phys. Rev. B94 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. B98 155104 [40] Furukawa S and Ueda M 2012 Phys. Rev. A86 031604 [41] Wu Y H and Jain J K 2013 Phys. Rev. B87 245123 [42] Wu Y L, Regnault N and Bernevig B A 2013 Phys. Rev. B110 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 Physics52 819 [58] Boening J, Filinov A and Bonitz M 2011 Phys. Rev. B84 075130 [59] Astrakharchik G E, Kurbakov I L, Sychev D V, et al. 2021 Phys. Rev. B103 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. B90 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. B32 5208 [64] Alicea J, Motrunich and Refael G F 2009 Phys. Rev. Lett.103 256403 [65] Anderson P W 1984 Phys. Rev. B30 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 Science305 5687 [69] Greiner M, Regal C A and Jin D S 2003 Nature426 537 [70] Zwierlein M W 2014 Superfluidity in ultracold atomic Fermi gases in Novel Superfluids2 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. B85 195113
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