Dresden 2003 – wissenschaftliches Programm
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HL: Halbleiterphysik
HL 26: Transport im hohen Magnetfeld/Quanten-Hall-Effekt
HL 26.1: Vortrag
Dienstag, 25. März 2003, 15:15–15:30, BEY/154
Non-abelian Quantum Statistics in the ν =5/2 Quantum Hall State — •Eros Mariani1,2, Ady Stern2, and Felix Von Oppen3 — 1I Institut fuer Theoretische Physik, Universitaet Hamburg (Germany) — 2The Weizmann Institute of Science, Rehovot (Israel) — 3FU Berlin (Germany)
In a seminal 1991 paper, Moore and Read proposed the ”Pfaffian state” as an approximate ground state for the ν =5/2 quantum Hall state, and discovered that the excitations of this ground state obey non-abelian statistics. Subsequent works, such as by Nayak and Wilczek (1996) studied how the non-abelian statistics results from the degeneracy of the ground state. For 2n quasiholes at fixed positions the ground state is 2n−1-degenerate, and interchanges of quasi-holes amount to unitary transformations in the 2n−1-dimensional Hilbert space of the ground states. Recently, Read and Green related the Pfaffian state to a p-wave superconductor of composite fermions, with the quasi-holes being vortices in that super-conductor. In this work we construct a physical picture that explains the non-abelian statistics by combining two ingredients. The first is the geometric phase accumulated by a vortex in a superconductor as it encircles a closed loop (or by two vortices as they interchange positions). This phase is 2π N, where N is the number of Cooper-pairs encircled by the vortex. The second is the quantum state of the zero-energy localized modes associated with each vortex in a p-wave superconductor. The explicit form of the BCS-like Ground State is presented, together with the identification of the Cooper-pairs.