$0\text{−}\pi$ phase shifts in Josephson junctions as a signature for the $s_{\pm }$-wave pairing state

We investigate Josephson junctions with superconducting ferropnictides, both in the diffusive and ballistic limit. We focus on the proposed $s_{\pm }$-wave state and find that the relative phase shift intrinsic to the $s_{\pm }$-wave state may provide $0\text{−}\pi$ oscillations in the Josephson current. This feature can be used to discriminate this pairing state from the conventional $s$-wave symmetry. The $0\text{−}\pi$ oscillations appear both as a function of the ratio of the interface resistances for each band and, more importantly, as a function of temperature, which greatly aids in their detection.

Figure 1

(Color online) Plot of the DOS at $x=0$ (at the $N\mid I$ interface) for thin $\left(d_N/{\xi }_S=0.2\right)$ and thick $\left(d_N/{\xi }_S=1.0\right)$ normal-metal regions. We have set $r_{\Delta }=0.5$ and considered several values of $r_{\gamma }$.

Figure 2

(Color online) (a) Plot of the critical current for an $s\text{-wave}\left|N\right|s$-wave and $s\text{-wave}\left|N\right|s_{\pm }$-wave junction, using $r_{\Delta }=1.0$ and $\left|{\Delta }_s/{\Delta }_1\right|=1.0$. (b) Plot of the critical current in the $s\text{-wave}\left|N\right|s_{\pm }$-wave case, using $\left|{\Delta }_s/{\Delta }_1\right|=0.5$. In both (a) and (b), we have set $d_N/{\xi }_S=1.0$.

Figure 3

(Color online) Critical current for a ballistic $s\text{-wave}\left|I\right|s_{\pm }$-wave Josephson junction as a function of the relative barrier strength $r_Z$. Interband coupling is neglected, and we have set $Z_1=6$, $T=0$, and $\left|{\Delta }_{\lambda }\right|=\left|{\Delta }_s\right|$. Inset: current-phase relation for selected values of $r_Z$, as indicated by the arrows in the main figure.

Figure 4

(Color online) Plot of the critical current as a function of temperature for an $s\text{-wave}\left|N\right|s_{\pm }$-wave junction, using $d_N/{\xi }_S=1.0$ and $\left|{\Delta }_s/{\Delta }_1\right|=0.5$. In (a), we have $r_{\Delta }=0.3$ while in (b) $r_{\Delta }=1.3$.