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

TL;DR

This paper develops a nonlinear dynamical theory for Abrikosov-Josephson vortices along grain boundaries in superconductors, providing exact solutions and analyzing their effects on current transport, microwave response, and resonance phenomena.

Contribution

It introduces an exact analytical model for the dynamics of AJ vortices on low-angle grain boundaries, including nonlinear voltage-current characteristics and resonance effects.

Findings

Exact solution for overdamped AJ vortex structure under arbitrary currents

Formulas for flux flow resistivity and nonlinear V-I characteristics

Identification of flux flow resonance and its impact on V-I behavior

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, $n\hbar\omega/2e$.