Thin-film Josephson junctions with alternating critical current density

Abstract

We study the field dependence of the maximum current ${I}_{m}(H)$ in narrow edge-type thin-film Josephson junctions with alternating critical current density. ${I}_{m}(H)$ is evaluated within nonlocal Josephson electrodynamics taking into account the stray fields that affect the difference of the order-parameter phases across the junction and therefore the tunneling currents. We find that the phase difference along the junction is proportional to the applied field, depends on the junction geometry, but is independent of the Josephson critical current density ${g}_{c}$, i.e., it is universal. An explicit form for this universal function is derived for small currents through junctions of the width $W⪡\ensuremath{\Lambda}$, the Pearl length. The result is used to calculate ${I}_{m}(H)$. It is shown that the maxima of ${I}_{m}(H)\ensuremath{\propto}1/\sqrt{H}$ and the zeros of ${I}_{m}(H)$ are equidistant but only in high fields. We find that the spacing between zeros is proportional to $1/{W}^{2}$. The general approach is applied to calculate ${I}_{m}(H)$ for a superconducting quantum interference device with two narrow edge-type junctions. If ${g}_{c}$ changes sign periodically or randomly, as it does in grain boundaries of high-${T}_{c}$ materials and superconductor-ferromagnet-superconductor heterostructures, ${I}_{m}(H)$ not only acquires the major side peaks, but due to nonlocality the following peaks decay much slower than in bulk junctions.