Gauge Theories of Josephson Junction Arrays

Abstract

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system, with an antisymmetric Kalb-Ramond gauge field.

39 pages, harvmac, two figures available on request

References in corpus (6)

• Bosonization of Fermi Systems in Arbitrary Dimension in Terms of Gauge Forms
• Quantum Hall Fluid of Vortices in a Two Dimensional Array of Josephson Junctions
• Self Duality and Oblique Confinement in Planar Gauge Theories
• Nonlinear Schrödinger Equation for Superconductors
• Vertex Operators for the BF System and its Spin-Statistics Theorems
• Implications of adiabatic phases for a vortex in a superconductor film

Cited by in corpus (62)

• Classification of topological insulators and superconductors in three spatial dimensions
• Quantum Link Models: A Discrete Approach to Gauge Theories
• On the existence of a Bose Metal at T=0
• Topological BF field theory description of topological insulators
• Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• Mutual Chern-Simons theory for Z_2 topological order
• Evolution of the Chern-Simons Vortices
• SU(2) slave-boson formulation of spin nematic states in S=1/2 frustrated ferromagnets
• Superinsulator-Superconductor Duality in Two Dimensions
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Superconductors with Topological Order
• Bosonic topological insulator intermediate state in the superconductor-insulator transition
• Quantum magnetic monopole condensate
• Duality and Massive Gauge Invariant Theories
• Confinement-deconfinement interplay in quantum phases of doped Mott insulators
• Direct probe of the interior of an electric pion in a Cooper pair superinsulator
• Topologically Massive Abelian Gauge Theory From BFT Hamiltonian Embedding of A First-order Theory
• On the dual equivalence of the Born-Infeld-Chern-Simons model coupled to dynamical U(1) charged matter
• Topological Nature of High Temperature Superconductivity
• On the dual equivalence of the self-dual and topologically massive $B\wedge F$ models coupled to dynamical fermionic matter
• Vogel-Fulcher-Tamman criticality of 3D superinsulators
• Higgsless superconductivity from topological defects in compact BF terms
• The superconductor-insulator transition in absence of disorder
• Magnetic monopoles and superinsulation in Josephson junction arrays
• Global room-temperature superconductivity in graphite
• Complex Monopoles in the Georgi-Glashow-Chern-Simons Model
• Weakly localised bosons
• Topological Order in Frustrated Josephson Junction Arrays
• Topological order in Josephson junction ladders with Mobius boundary conditions
• Superconducting Topological Fluids in Josephson Junction Arrays
• On the dual equivalence of the self-dual and topologically massive p-form models
• Hall viscosity and conductivity of two-dimensional chiral superconductors
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• Circuit QED-based measurement of vortex lattice order in a Josephson junction array
• Minimal coupling of the Kalb-Ramond field to a scalar field
• Non-Chern-Simons Topological Mass Generation in (2+1) Dimensions
• Chern-Simons theory on the lattice
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Superconductivity in Mutual Chern-Simons Gauge Theory
• Disordered BKT transition and superinsulation
• Fermion-fermion duality in 3+1 dimensions
• Origin of Topological Order in a Cooper Pair Insulator
• Duality and Confinement in Massive Antisymmetric Tensor Gauge Theories
• Gauge Invariant Factorisation and Canonical Quantisation of Topologically Massive Gauge Theories in Any Dimension
• Fully frustrated Josephson junction ladders with Mobius boundary conditions as topologically protected qubits
• U_e(1)xU_g(1) Actions in 2+1-Dimensions: Full Vectorial Electric and Magnetic Fields
• The Fate of the Photon in Topological Matter: Superconductivity, Confinement and the Vortex Quantum Hall Effect
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Characterizing Topological Order in Superconducting Systems
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Topologically protected qubits as minimal Josephson junction arrays with non trivial boundary conditions: a proposal
• Spin-flux attachment by dimensional reduction of vortices
• Emergent Higgsless Superconductivity
• On the Doubling Phenomenon in Lattice Chern-Simons Theories
• Spin-Charge Soldering from Tensor Higgs mechanism
• Theoretical proposal for dual transformation between the Josephson effect and quantum phase slip in single junction systems and nanowires
• Minimal Models for a Superconductor-Insulator Conformal Quantum Phase Transition
• Vortices in a parity-invariant Maxwell-Chern-Simons model
• Self-dual Maxwell-Chern-Simons solitons in a parity-invariant scenario
• Topological Quantum Phase Transitions in Topological Superconductors
• Mass Generation in Abelian U(1) Gauge Theories: A Rich Network of Dualities