2007/11/30 by Parsa Bonderson, J. K. Slingerland · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.78.125323
published as Phys. Rev. B 78, 125323 (2008) · 10 pages; v2: many additional details and discussion included to help clarify the original results, including a composite fermion type formulation of some of the states; v3: minor corrections
arxiv created 2008/09/18 · openalex publication_date 2008/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the \ensuremathν=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.