Bonderson, Parsa and Slingerland, J.K.
Fractional quantum Hall hierarchy and the second Landau level.
Physical Review B, 78 (125323).
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian,
fractional quantum Hall states. Applying this to the v=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.
||Original article published in Physical Review B Vol.78 No.125323(2008) © 2008 The American Physical Society. We thank Jim Eisenstein, Adrian Feiguin, Woowon Kang,
Chetan Nayak, Wei Pan, Ed Rezayi, Kirill Shtengel, and
Steve Simon for illuminating discussions. We also acknowledge
the hospitality of the IQI, Microsoft Station Q, and the
Aspen Center for Physics. This work was supported in part
by the NSF under Grant No. PHY-0456720 and the ARO
under Contract No. W911NF-05-1-0294.
||Fractional; quantum Hall hierarchy; second Landau level;
||Faculty of Science and Engineering > Mathematical Physics
Dr. Joost Slingerland
||27 Sep 2011 13:28
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||Physical Review B
||American Physical Society
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