Observation of double resistance anomalies and excessive resistance in mesoscopic superconducting Au 0.7 In 0.3 rings with phase separation

We have measured mesoscopic superconducting ${\mathrm{Au}}_{0.7}{\mathrm{In}}_{0.3}$ rings prepared by $e$-beam lithography and sequential deposition of Au and In at room temperature followed by a standard lift-off procedure. The majority of the samples are found to exhibit highly unusual double resistance anomalies, two resistance peaks with the peak resistances larger than the normal-state resistance, near the onset of superconductivity in the $R(T)$ (resistance vs temperature) curves, and an $h∕2e$ resistance oscillation with a very small amplitude. A magnetic field applied perpendicular to the ring plane appears to suppress the low-temperature peak easily, but only broadens the high-temperature peak. In the intermediate-field range, the high-temperature resistance peak becomes flat down to the lowest temperature, resulting apparently in a magnetic-field-induced metallic state with its resistance higher than the normal-state resistance, referred to here as excessive resistance. The dynamical resistance vs bias current measurements carried out in samples showing double resistance anomalies suggest that there are two critical currents in these samples. We attribute the double resistance anomalies and the two critical currents to the presence of two superconducting phases originating from the phase separation of ${\mathrm{Au}}_{0.7}{\mathrm{In}}_{0.3}$ in which In-rich grains of AuIn precipitate in a uniform In-dilute matrix of ${\mathrm{Au}}_{0.9}{\mathrm{In}}_{0.1}$. The local superconducting transition temperature of the In-rich grains is higher than that of the In-dilute matrix. The double resistance anomalies are not found in a sample showing the conventional $h∕2e$ Little-Parks (LP) resistance oscillation, which we believe is due to the absence of the phase separation in this particular sample. Finally, we argue that the $h∕2e$ resistance oscillation observed in samples showing double resistance anomalies is not the LP but rather the Altshuler-Aronov-Spivak resistance oscillation of normal electrons enhanced by superconductivity.