Josephson Coupled Moore-Read States

Abstract

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.~{\bf 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 $U(1{)}_2\times U(1{)}_2$ 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 $U(1{)}_4\times U(1)$ structure.

20 pages, 4 figures, 3 tables

References in corpus (27)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Fractional quantum Hall states at zero magnetic field
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Fractional quantum Hall effect in the absence of Landau levels
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Condensate induced transitions between topologically ordered phases
• Genons, twist defects, and projective non-Abelian braiding statistics
• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
• Robustness of a perturbed topological phase
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• A theory of topological edges and domain walls
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Paired composite fermion wavefunctions
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Optical lattice quantum Hall effect
• Adiabatic continuity between Hofstadter and Chern insulator states
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• Trial wavefunctions for the Goldstone mode in ν=1/2+1/2 quantum Hall bilayers

Cited by in corpus (1)

• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders