Berlin 2008 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 24: Correlated Electrons: Low-dimensional Systems - Models

TT 24.1: Vortrag

Mittwoch, 27. Februar 2008, 14:00–14:15, H 2053

Particle-hole symmetry and the Pfaffian state — •Bernd Rosenow, Michael Levin, and Bertrand I. Halperin — Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

The Moore-Read Pfaffian (Pf) state is believed to be a strong candidate for the observed quantum Hall plateau at filling fraction ν=5/2. This possibility is particularly exciting since the quasiparticle excitations in this state carry non-abelian statistics. Much work has been devoted to understanding the basic physical properties of the Pf state. However, one aspect of the Pf state has not been addressed - namely, its behavior under particle-hole (PH) conjugation of electrons in the spin-aligned partially occupied second Landau level. This issue is important because, to a good approximation, the Hamiltonian of the ν = 5/2 FQH system is symmetric under this PH conjugation.

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 by both their bulk and edge physics though the difference is most dramatic at the edge: the edge of the anti-Pfaffian state has a composite structure that leads to a different thermal Hall conductance and different tunneling exponents than the Pfaffian state. At the same time, the two states are exactly degenerate in energy for a ν=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed σ_xy = 5/2(e²/h) quantum Hall plateau.