Nonmonotonic temperature dependence of critical current in diffusive $d$-wave junctions

We study the Josephson effect in D/I/DN/I/D junctions, where I, DN, and D denote an insulator, a diffusive normal metal, and a $d$-wave superconductor, respectively. The Josephson current is calculated based on the quasiclassical Green’s function theory with a general boundary condition for unconventional superconducting junctions. In contrast to $s$-wave junctions, the product of the Josephson current and the normal-state resistance is enhanced by making the interface barriers stronger. The Josephson current has a nonmonotonic temperature dependence due to the competition between the proximity effect and the midgap Andreev resonant states.

Figure 1

(Color online) Schematic illustration of the model.

Figure 2

(Color online) (a) Temperature dependence of $I_{C}R$ for $(\alpha ,\beta )=(0,0)$. (b) The results for $s$-wave junctions for comparison. Real (c) and imaginary (d) parts of ${\Phi }_{\omega }$ as a function of $\omega$. Here we choose $R_d∕R_b=1$ and $E_{Th}∕\Delta \left(0\right)=1$.

Figure 3

(Color online) Temperature dependence of (a) $I_{C}R$ at $Z=10$ for several orientation angles. (b) $I_{C}R$ at $(\alpha ,\beta )=(\pi ∕8,0)$ for several $Z$ values. Real and imaginary parts of ${\Phi }_{\omega }$ as a function of $\omega$ for $(\alpha ,\beta )=(\pi ∕8,0)$ and $\phi =\pi ∕2$ at $x=L∕2$ are shown in (c) and (d), respectively. Here we choose $R_d∕R_b=1$ and $E_{Th}∕\Delta \left(0\right)=1$.

Figure 4

The peak temperature as a function of $R_d∕R_b$ (a) and $E_{Th}∕\Delta \left(0\right)$ (b) for $Z=10$ and $(\alpha ,\beta )=(\pi ∕8,0)$.