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Josephson-coupled Moore-Read states

Möller, Gunnar, Hormozi, Layla, Slingerland, Joost, Simon, Steven H (2014) Josephson-coupled Moore-Read states. Physical Review B: Condensed Matter and Materials Physics, 90 (23). p. 235101. ISSN 0163-1829. (doi:10.1103/PhysRevB.90.235101) (KAR id:55593)


We study a quantum Hall bilayer system of bosons at total filling factor nu = 1, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions.

We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys. Rev. Lett. 108, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with U(1)_2 x U(1)_2 topological order, but it is realized in the symmetric/antisymmetric-basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected U(1)_4 x U(1) structure.

Item Type: Article
DOI/Identification number: 10.1103/PhysRevB.90.235101
Uncontrolled keywords: Physics of Quantum Materials, fractional quantum Hall, superconductor, Josephson effect, exactly solvable models, Physics of Quantum Materials
Subjects: Q Science > QC Physics > QC173.45 Condensed Matter
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Funders: Organisations -1 not found.
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Isaac Newton Trust (
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Science Foundation Ireland (
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Depositing User: Gunnar Moeller
Date Deposited: 18 Aug 2016 21:29 UTC
Last Modified: 09 Dec 2022 07:55 UTC
Resource URI: (The current URI for this page, for reference purposes)

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