2014/09/22 by Gunnar Möller, Layla Hormozi, Joost Slingerland +1
Physics and Astronomy · #Antisymmetric relation #Boson #Condensed matter physics #Hamiltonian (control theory) #Josephson effect #Mathematical physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Quantum tunnelling #Quasiparticle #Superconductivity #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.90.235101
published as Phys. Rev. B 90, 235101 (2014) · 20 pages, 4 figures, 3 tables
arxiv created 2014/09/22 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a quantum Hall bilayer system of bosons at total filling factor \ensuremathν=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\ifmmode×\else\texttimes\fiU(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\ifmmode×\else\texttimes\fiU(1) structure.