Field theoretical model of multi-layered Josephson junction and dynamics of Josephson vortices

Abstract

Multi-layered Josephson junctions are modeled in the context of a field theory, and dynamics of Josephson vortices trapped inside insulators are studied. Starting from a theory consisting of complex and real scalar fields coupled to a U(1) gauge field which admit parallel $N-1$ domain-wall solutions, Josephson couplings are introduced weakly between the complex scalar fields. The $N-1$ domain walls behave as insulators separating $N$ superconductors, where one of the complex scalar fields has a gap. We construct the effective Lagrangian on the domain walls, which reduces to a coupled sine-Gordon model for well-separated walls We then construct sine-Gordon solitons emerging in an effective theory in which we identify Josephson vortices carrying singly quantized magnetic fluxes. When two neighboring superconductors tend to have the same phase, the ground state does not change with the positions of domain walls. On the other hand, when two neighboring superconductors tend to have $\pi$-phase differences, the ground state has a phase transition depending on the positions of domain walls; when the two walls are close to each other, frustration occurs because of the coupling between the two superconductors besides the thin superconductor. Focusing on the case of three superconductors separated by two insulators, we find for the former case that the interaction between two Josephson vortices on different insulators changes its nature, i.e., attractive or repulsive, depending on the positions of the domain walls. In the latter case, there emerges fractional Josephson vortices when two degenerate ground states appear due to spontaneous charge-symmetry breaking, and the number of the Josephson vortices varies with the position of the domain walls. Our predictions should be verified in multilayered Josephson junctions.

25 pages, 17 figures, Animation of magnetic flux distribution is included as an ancillary file

References in corpus (23)

• Bipolar supercurrent in graphene
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Observation of Leggett's collective mode in a multi-band MgB2 superconductor
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Magnetic response of mesoscopic superconducting rings with two order parameters
• Imaging Josephson Vortices on the Surface Superconductor Si(111)-(root7xroot3)-In using a Scanning Tunneling Microscope
• Ginzburg-Landau theory for multiband superconductors: microscopic derivation
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Josephson vortices and the Atiyah-Manton construction
• Webs of Walls
• Domain Walls with Non-Abelian Clouds
• Non-Abelian Sine-Gordon Solitons
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Phase soliton and pairing symmetry of a two-band superconductor: Role of the proximity effect
• Effective Action of Domain Wall Networks
• Josephson Effects in Three-Band Superconductors with Broken Time-Reversal Symmetry
• Dynamics of Strings between Walls
• Chiral sine-Gordon model
• Skyrmionic vortex lattices in coherently coupled three-component Bose-Einstein condensates
• Vortices with Fractional Flux Quanta in Multi-Band Superconductors
• Dynamics of Strings between Domain Walls

Cited by in corpus (9)

• Relations among topological solitons
• Domain Wall Skyrmions in Chiral Magnets
• Chiral Magnets from String Theory
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Exhausting all exact solutions of BPS domain wall networks in arbitrary dimensions
• Chemical bonds of two vortex species with a generalized Josephson term and arbitrary charges
• Exact solutions of domain wall junctions in arbitrary dimensions
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Long-time soliton dynamics via a coarse-grained space-time method