Nonlinear dynamics of vortices in easy flow channels along grain boundaries in superconductors

Abstract

A theory of nonlinear dynamics of mixed Abrikosov vortices with Josephson cores (AJ vortices) on low-angle grain boundaries (GB) in superconductors is proposed. Dynamics and pinning of AJ vortices determine the in-field current transport through GB and the microwave response of polycrystal in the crucial misorientation range $\vartheta <20-30^{\circ }$ of the exponential drop of the local critical current density $J_b(\vartheta )$ through GB. An exact solution for an overdamped periodic AJ vortex structure driven along GB by an arbitrary time dependent transport current in a dc magnetic field $H>H_{c1}$ is obtained. The dynamics of the AJ vortex chain is parameterized by solutions of two coupled first order nonlinear differential equations which describe self-consistently the time dependence of the vortex velocity and the AJ core length. Exact formulas for the dc flux flow resistivity $R_f(H)$, and the nonlinear voltage-current characteristics are obtained. Dynamics of the AJ vortex chain driven by superimposed ac and dc currents is considered, and general expressions for a linear complex resistivity $R(\omega )$ and dissipation of the ac field are obtained. A flux flow resonance is shown to occur at large dc vortex velocities $v$ for which the imaginary part of $R(\omega )$ has peaks at the "washboard" ac frequency ${\omega }_0=2\pi v/a$, where $a$ is the inter vortex spacing. This resonance can cause peaks and portions with negative differential conductivity on the averaged dc voltage-current (V-I) characteristics. Ac currents of large amplitude cause generation of higher voltage harmonics and phase locking effects which manifest themselves in steps on the averaged dc I-V curves at the Josephson voltages, $n\hslash \omega /2e$.

17 pages, 9 figures. submitted to Phys. Rev. B

References in corpus (3)

• Flux flow of Abrikosov-Josephson vortices along grain boundaries in high-temperature superconductors
• Vortex Channeling and the V-I Characteristic of YBa2Cu3O7 Low Angle Grain Boundaries
• Critical Current Density of YBa{2}Cu{3}O{7-d} Low-Angle Grain Boundaries in Self-Field

Cited by in corpus (12)

• Dynamics of vortex penetration, jumpwise instabilities and nonlinear surface resistance of type-II superconductors in strong rf fields
• Laser Scanning Microscopy of HTS Films and Devices
• Phase textures induced by dc current pairbreaking in multilayer structures and two-gap superconductors
• Depinning and dynamics of vortices confined in mesoscopic flow channels
• Dynamic transition of vortices into phase slips and generation of vortex-antivortex pairs in thin film Josephson junctions under dc and ac currents
• Dynamics of single vortices in grain boundaries: I-V characteristics on the femto-volt scale
• Tuning microwave losses in superconducting resonators
• Plastic depinning in artificial vortex channels: competition between bulk and boundary nucleation
• Strong improvement of the transport characteristics of YBa${}_{\text{2}}$Cu${}_{\text{3}}$O${}_{\text{7-x}}$ grain boundaries using ionic liquid gating
• Nonlinear dynamics of Josephson vortices in a film screen under dc and ac magnetic fields
• Microwave properties of DyBCO monodomain in the mixed state and comparison with other RE-BCO systems
• Measurements of microwave vortex response in dc magnetic fields in Tl${}_2$Ba${}_2$CaCu${}_2$O${}_{8+x}$ films