Particle-hole symmetry and the ν=5/2 Quantum Hall state

被引:353
作者
Lee, Sung-Sik [1 ]
Ryu, Shinsei
Nayak, Chetan
Fisher, Matthew P. A.
机构
[1] Univ Calif Santa Barbara, Kavli Inst Theoret Phys, Santa Barbara, CA 93106 USA
[2] Univ Calif Santa Barbara, Stn Q, Santa Barbara, CA 93106 USA
[3] Univ Calif Los Angeles, Dept Phys & Astron, Los Angeles, CA 90095 USA
基金
美国国家科学基金会;
关键词
D O I
10.1103/PhysRevLett.99.236807
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.
引用
收藏
页数:4
相关论文
共 27 条
[1]   Detecting non-Abelian statistics in the ν=5/2 fractional quantum Hall state -: art. no. 016803 [J].
Bonderson, P ;
Kitaev, A ;
Shtengel, K .
PHYSICAL REVIEW LETTERS, 2006, 96 (01)
[2]   Topologically protected qubits from a possible non-Abelian fractional quantum Hall state [J].
Das Sarma, S ;
Freedman, M ;
Nayak, C .
PHYSICAL REVIEW LETTERS, 2005, 94 (16)
[3]   Insulating and fractional quantum Hall states in the first excited Landau level [J].
Eisenstein, JP ;
Cooper, KB ;
Pfeiffer, LN ;
West, KW .
PHYSICAL REVIEW LETTERS, 2002, 88 (07) :768011-768014
[4]   Edge states and tunneling of non-Abelian quasiparticles in the ν=5/2 quantum Hall state and p+ip superconductors [J].
Fendley, Paul ;
Fisher, Matthew P. A. ;
Nayak, Chetan .
PHYSICAL REVIEW B, 2007, 75 (04)
[5]   Dynamical disentanglement across a point contact in a non-abelian quantum hall state [J].
Fendley, Paul ;
Fisher, Matthew P. A. ;
Nayak, Chetan .
PHYSICAL REVIEW LETTERS, 2006, 97 (03)
[6]   A Chern-Simons effective field theory for the Pfaffian quantum Hall state [J].
Fradkin, E ;
Nayak, C ;
Tsvelik, A ;
Wilczek, F .
NUCLEAR PHYSICS B, 1998, 516 (03) :704-718
[7]   PARTICLE-HOLE SYMMETRY IN THE ANOMALOUS QUANTUM HALL-EFFECT [J].
GIRVIN, SM .
PHYSICAL REVIEW B, 1984, 29 (10) :6012-6014
[8]   PAIRED HALL STATES [J].
GREITER, M ;
WEN, XG ;
WILCZEK, F .
NUCLEAR PHYSICS B, 1992, 374 (03) :567-614
[9]   4-FERMI THEORIES IN FEWER THAN 4 DIMENSIONS [J].
HANDS, S ;
KOCIC, A ;
KOGUT, JB .
ANNALS OF PHYSICS, 1993, 224 (01) :29-89
[10]   Non-abelian statistics of half-quantum vortices in p-wave superconductors [J].
Ivanov, DA .
PHYSICAL REVIEW LETTERS, 2001, 86 (02) :268-271