Nonlocal electrodynamics of normal and superconducting films

TL;DR

This paper develops a formalism based on Maxwell's equations to analyze the nonlocal electrodynamics of normal and superconducting films, capturing complex phenomena like flux trapping, avalanches, and patterned structures with both analytical and numerical methods.

Contribution

It introduces a comprehensive formalism for modeling nonlocal electrodynamics in films, including analytical solutions for Ohmic films and numerical simulations for superconducting behaviors.

Findings

Analytical solution for Ohmic film response to delta source-field

Numerical simulation of flux dynamics and avalanches in superconducting films

Demonstration of flux patterns in patterned superconducting structures

Abstract

Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modelled and analyzed. The formalism is based on the Maxwell equations, and a material current-voltage characteristics, linear for normal metals, and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function source-field turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain, in both Fourier and real space. Next, the dynamical behaviour of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic avalanches. The avalanches tend to invade the central part where the density of trapped flux is largest, forming dendritic patterns in excellent agreement with magneto-optical images. Detailed profiles of current and flux density are presented and discussed. Finally, the formalism is extended to multiply connected samples, and numerical results for a patterned superconducting film, a ring with a square lattice of antidots, are presented and discussed.