Superconducting junction with tri-component pairing gap functions

Abstract

We study a superconducting hetro-junction with one side characterized by the unconventional chiral $p$-wave gap function $p_x\pm i{p}_y$ and the other side the conventional $s$-wave one. Though a relative phase of $\pm \frac{\ddot{I}}{€}2$ between any two components of gap functions is favored in the junction region, mutual phase differences cannot achieve $\pm \frac{\ddot{I}}{€}2$ simultaneously, which results in frustration. Based on a Ginzburg-Landau free energy analysis, the frustrated pattern is determined to be $s+i\hat{I}{\cdot }_1(e^{i\hat{I}{\cdot }_2\ddot{I}†/2}{p}_x+\hat{I}{\cdot }_3{e}^{-i\hat{I}{\cdot }_2\ddot{I}†/2}{p}_y)$ with $\hat{I}{\cdot }_j=\pm 1$ ($j=1,2,3$), where $\ddot{I}†$ is the phase difference between the $p_x$- and $p_y$-wave gap functions. Furthermore, we find that the junction exhibits an anisotropic magnetoelectric effect, manifesting itself as an anisotropic spin magnetization along the edge of the junction.

12 pages