Anomalous Josephson network in the Ru-Sr2RuO4 eutectic system

We measured the $c$-axis current-voltage $(I\text{\penalty1000-\hskip0pt}V)$ characteristics of ${\mathrm{Sr}}_{2}{\mathrm{Ru}\mathrm{O}}_{4}$ and Ru-enriched ${\mathrm{Sr}}_{2}{\mathrm{Ru}\mathrm{O}}_{4}$ eutectic systems. Our results revealed that the 3-K phase in the $\mathrm{Ru}\text{\penalty1000-\hskip0pt}{\mathrm{Sr}}_{2}{\mathrm{Ru}\mathrm{O}}_{4}$ eutectic system forms a complex Josephson network, which dominates the critical current of the system even at temperatures below bulk ${T}_{c}$. We also found that this Josephson network exhibits anomalous asymmetric features in $I\text{\penalty1000-\hskip0pt}V$ characteristics, such that the critical current density at positive current ${J}_{c}^{\phantom{\rule{0.2em}{0ex}}+}$ differs from that at negative current ${J}_{c}^{\phantom{\rule{0.2em}{0ex}}\ensuremath{-}}$ by 5% at 0.3 K. This unusual behavior diminishes with increasing temperature or magnetic field. It disappears at temperatures above 2.3 K at zero field, or above 0.2 T at 0.3 K. We discuss these unusual behaviors in terms of a recent theory that argues a time reversal symmetry breaking transition in the 3-K phase.