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Josephson-coupled Moore-Read states



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Möller, G 
Hormozi, L 
Slingerland, J 
Simon, SH 


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 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.



5108 Quantum Physics, 51 Physical Sciences, 5104 Condensed Matter Physics

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Physical Review B - Condensed Matter and Materials Physics

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American Physical Society (APS)
The Royal Society (uf120157)
Leverhulme Trust (ECF-2011-565)
The authors would like to thank Nordita and the Aspen Center for Physics their hospitality, and acknowledge support from the Leverhulme Trust under grant ECF-2011-565, the Newton Trust of the University of Cambridge and by the Royal Society under grant UF120157 (G.M.), the European Union under Marie Curie award 299890 QETPM (L.H.), Science Foundation Ireland principal investigator awards 08/IN.1/I1961 and 12/IA/1697 (J.K.S.) and EPSRC grant EP/I032487/1 (S.H.S.).