Temporal evolution of electric transport properties of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{O}_{7-\delta }$ Josephson junctions produced by focused-helium-ion-beam irradiation

We examined the temporal evolution of Josephson and resistive barriers created by a 30-keV focused helium ion beam in microbridges of epitaxially grown single-crystal ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{O}_{7-\delta }$ thin films. Repeated electric transport measurements at 4.2 K within 300 days after irradiation revealed an increase in the critical current density $j_c$ for devices stored at room temperature under nitrogen atmosphere. This behavior can be described by a diffusion-based model of displaced chain oxygen moving back to original lattice sites, thus healing the barrier and partially restoring critical current. We find that $j_c\propto \exp (-\sqrt{t/\tau })$ with time $t$. The relaxation time $\tau$ increases exponentially with helium irradiation dose and can exceed several hundred days for high-quality Josephson junctions. To achieve higher diffusion rates and thus shorter relaxation times, we annealed some devices in different oxygen partial pressures, right after irradiation. Within a week, those junctions relaxed to a quasistable state, making this a feasible option to achieve temporal stability of device parameters.