Particle-Hole Symmetry and the Pfaffian State

Abstract

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a nu=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed sigma_{xy}=5/2(e;{2}/h) quantum Hall plateau.

Fractional quantum Hall hierarchy and the second Landau level

“…[15][16][17][18][19][20] Recent tunneling shot-noise experiments have confirmed the e / 4 fundamental quasihole charge of the =5/ 2 state expected for the MR state. 21 Further recent evidence from the scaling behavior in dc transport experiments 22 at =5/ 2 best agrees with the particle-hole conjugate of MR. 23,24 Although the remaining observed filling fractions in the second Landau level have odd denominators, numerics indicate that the electron correlations for 7 / 3 Յ Յ 8 / 3 have a non-Laughlin character similar to that of =5/ 2, 25 and so only =14/ 5 is expected to be an Abelian state. Aside from the Abelian hierarchy states, the non-Abelian Read-Rezayi ͑RR͒ k-body clustered states 26 ͑which include MR͒ and their particle-hole conjugates are essentially the only single layer spin-polarized descriptions that have been proposed for these FQH plateaus.…”

Fractional quantum Hall effect in a tilted magnetic field

“…This is unfortunate because some of the most exciting FQH states are realized in n = 1 LL, such as the celebrated ν = 5/2 15 and ν = 12/5 16 states that are believed to possess non-Abelian quasiparticles in the bulk 6,17 . In the case of half filling, LL mixing is the mechanism that breaks the particlehole symmetry, and selects one of the two candidate wavefunctions proposed for it 6,[18][19][20] . More accurate treatment of LL mixing has inspired some recent work 14,21 , but in general its effects on various filling factors are still poorly understood.…”

Influence of device geometry on tunneling in theν=52quantum Hall liquid

“…Both Abelian and non-Abelian candidate states were proposed as possible theoretical explanations of the 5/2 FQH effect 2,[5][6][7][8][9][10][11][12] . A number of methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] were invented and several experiments [29][30][31][32][33][34][35][36][37][38][39][40] were performed in an attempt to determine the right ground state.…”