Fractional quantum Hall hierarchy and the second Landau level

Parsa Bonderson and J. K. Slingerland
Phys. Rev. B 78, 125323 – Published 26 September 2008

Abstract

We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the ν=5/2 Moore-Read state, we construct explicit trial wave functions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.

  • Received 24 July 2008

DOI:https://doi.org/10.1103/PhysRevB.78.125323

©2008 American Physical Society

Authors & Affiliations

Parsa Bonderson1,2 and J. K. Slingerland2,3,4,5

  • 1Microsoft Research, Station Q, Elings Hall, University of California, Santa Barbara, California 93106, USA
  • 2California Institute of Technology, Pasadena, California 91125, USA
  • 3Dublin Institute for Advanced Studies, School for Theoretical Physics, 10 Burlington Road, Dublin 4, Ireland
  • 4Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland
  • 5Department of Physics, University of California, Riverside, California 92521, USA

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Issue

Vol. 78, Iss. 12 — 15 September 2008

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