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 (68)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Quantum state engineering with Josephson-junction devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• String-net condensation: A physical mechanism for topological phases
• Majorana fermions in a tunable semiconductor device
• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Condensate induced transitions between topologically ordered phases
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Genons, twist defects, and projective non-Abelian braiding statistics
• The Fractional Quantum Hall effect in an array of quantum wires
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• From Luttinger liquid to non-Abelian quantum Hall states
• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
• Observation of a Linearly Dispersing Collective Mode in a Quantum Hall Ferromagnet
• Robustness of a perturbed topological phase
• Edge excitations of paired fractional quantum Hall states
• Three-dimensional topological lattice models with surface anyons
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• High field fractional quantum Hall effect in optical lattices
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Wire deconstructionism of two-dimensional topological phases
• A theory of topological edges and domain walls
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory
• Majorana edge states in two atomic wires coupled by pair-hopping
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Paired composite fermion wavefunctions
• Spontaneous Interlayer Coherence in Double-Layer Quantum Hall Systems: Symmetry Breaking Interactions, In-Plane Fields and Phase Solitons
• Phase transitions in topological lattice models via topological symmetry breaking
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting
• Optical lattice quantum Hall effect
• Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
• Broken quantum symmetry and confinement phases in planar physics
• Adiabatic continuity between Hofstadter and Chern insulator states
• The Broken Symmetry of Two-Component $\nu =1/2$ Quantum Hall States
• Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• Stabilization of the p-wave superfluid state in an optical lattice
• Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux
• 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
• Unpaired composite fermion, topological exciton, and zero mode
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• On the stability of topological phases on a lattice
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Condensate-induced transitions and critical spin chains
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Lieb-Schultz-Mattis theorem for quasi-topological systems
• A hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points
• Trial wavefunctions for the Goldstone mode in ν=1/2+1/2 quantum Hall bilayers

Cited by in corpus (11)

• Anyon condensation and its applications
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Model Fractional Chern Insulators
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Competing topological orders in three dimensions: X-cube versus toric code
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Quantum phase transitions in the $K$-layer Ising toric code
• Dihedral twist liquid models from emergent Majorana fermions