Moller, Gunnar and Hormozi, Layla and Slingerland, Joost and Simon, Steven H. (2014) Josephson-Coupled Moore-Read States. Physical Review B, 90 (235101). pp. 1-19. ISSN 1098-0121

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Abstract

We study a quantum Hall bilayer system of bosons at total filling factor ν = 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×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×U(1) structure.

Item Type:	Article
Additional Information:	The definitive version of this article is available at Josephson-coupled Moore-Read states Gunnar Möller, Layla Hormozi, Joost Slingerland, and Steven H. Simon Phys. Rev. B 90, 235101 – Published 1 December 2014 . DOI: http://dx.doi.org/10.1103/PhysRevB.90.235101
Keywords:	Josephson-Coupled; Moore-Read States; quantum Hall bilayer system;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	6307
Identification Number:	https://doi.org/10.1103/PhysRevB.90.235101
Depositing User:	Dr. Joost Slingerland
Date Deposited:	20 Aug 2015 12:12
Journal or Publication Title:	Physical Review B
Publisher:	American Physical Society
Refereed:	Yes
URI:	http://journals.aps.org/prb
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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