Supergap and subgap enhanced currents in asymmetric {S_1FS_2} Josephson junctions

TL;DR

This paper theoretically investigates how asymmetric superconducting gaps in Josephson junctions influence supercurrent, revealing significant enhancements and the roles of supergap and subgap components in different regimes.

Contribution

It provides a comprehensive analysis of supercurrent behavior in asymmetric Josephson junctions, highlighting the importance of supergap and subgap contributions in ballistic and diffusive systems.

Findings

Supercurrent can be enhanced by over 100% in ballistic systems with increasing gap ratio.

Supercurrent in diffusive systems is enhanced by more than 50% and saturates with gap increase.

Second harmonics emerge due to subgap and supergap current competition in ferromagnetic junctions.

Abstract

We have theoretically studied the supercurrent profiles in three-dimensional normal metal and ferromagnetic Josephson configurations, where the magnitude of the superconducting gaps in the superconducting leads are unequal, i.e., $\Delta_1\neq \Delta_2$, creating asymmetric $S_1NS_2$ and $S_1FS_2$ systems. Our results reveal that by increasing the ratio of the superconducting gaps $\Delta_2/\Delta_1$, the critical supercurrent in a ballistic $S_1NS_2$ system can be enhanced by more than $100\%$, and reaches a saturation point, or decays away, depending on the junction thickness, magnetization strength, and chemical potential. The total critical current in a diffusive $S_1NS_2$ system was found to be enhanced by more than $50\%$ parabolically, and reaches saturation by increasing one of the superconducting gaps. In a uniform ferromagnetic junction, the supercurrent undergoes reversal by increasing $\Delta_2/\Delta_1>1$. Through decomposing the total supercurrent into its supergap and subgap components, our results illustrate their crucial relative contributions to the Josephson current flow. It was found that the competition of subgap and supergap currents in a $S_1FS_2$ junction results in the emergence of second harmonics in the current-phase relation. In contrast to a diffusive asymmetric Josephson configuration, the behavior of the supercurrent in a ballistic system with $\Delta_2/\Delta_1=1$ can be properly described by the subgap current component only, in a wide range of parameter sets, including Fermi level mismatch, magnetization strength, and junction thickness. Interestingly, when $\Delta_2/\Delta_1>1$, our results have found multiple parameter sets where the total supercurrent is driven by the supergap component. Therefore, our comprehensive study highlights the importance of subgap and supergap supercurrent components in both the ballistic and diffusive regimes.