Influence of magnetic impurities on charge transport in diffusive-normal-metal/superconductor junctions

Charge transport in the diffusive normal metal (DN)/insulator/$s$- and $d$-wave superconductor junctions is studied in the presence of magnetic impurities in DN in the framework of the quasiclassical Usadel equations with the generalized boundary conditions. The cases of $s$- and $d$-wave superconducting electrodes are considered. The junction conductance is calculated as a function of a bias voltage for various parameters of the DN metal, resistivity, Thouless energy, the magnetic impurity scattering rate, and the transparency of the insulating barrier between DN and a superconductor. It is shown that the proximity effect is suppressed by magnetic impurity scattering in DN for any value of the barrier transparency. In low-transparent $s$-wave junctions this leads to the suppression of the normalized zero-bias conductance. In contrast to that, in high transparent junctions zero-bias conductance is enhanced by magnetic impurity scattering. The physical origin of this effect is discussed. For the $d$-wave junctions, the dependence on the misorientation angle $\alpha$ between the interface normal and the crystal axis of a superconductor is studied. The zero-bias conductance peak is suppressed by the magnetic impurity scattering only for low transparent junctions with $\alpha \sim 0$. In other cases the conductance of the $d$-wave junctions does not depend on the magnetic impurity scattering due to strong suppression of the proximity effect by the midgap Andreev resonant states.

Figure 1

Schematic illustration of the model.

Figure 2

Normalized conductance for $Z=3$.

Figure 3

Normalized conductance for $Z=1$.

Figure 4

Normalized conductance for high transparent junctions with $Z=0$.

Figure 5

Real (upper panels) and imaginary (lower panels) part of ${\theta }_L$ for $Z=3$ and $E_{\mathrm{Th}}∕\Delta =1$.

Figure 6

Real (upper panels) and imaginary (lower panels) part of ${\theta }_L$ for $Z=3$ and $E_{\mathrm{Th}}∕\Delta =0.01$.

Figure 7

Real (upper panels) and imaginary (lower panels) parts of ${\theta }_L$ for high transparent junctions with $Z=0$ and $E_{\mathrm{Th}}∕\Delta =1$.

Figure 8

Real (upper panels) and imaginary (lower panels) parts of ${\theta }_L$ for high transparent junctions with $Z=0$ and $E_{\mathrm{Th}}∕\Delta =0.01$.

Figure 9

Normalized resistance for $Z=0$ and $E_{\mathrm{Th}}∕\Delta =0.01$.

Figure 10

Normalized zero voltage resistance as a function of $R_d∕R_b$.

Figure 11

Real part of ${\theta }_L$ at zero energy as a function of $R_d∕R_b$.

Figure 12

Normalized conductance in a $d$-wave junction for $Z=10$, $R_d∕R_b=1$, $E_{\mathrm{Th}}∕\Delta =0.01$, and $\alpha ∕\pi =0$.

Figure 13

Normalized conductance in a $d$-wave junction for $Z=10$, $R_d∕R_b=1$, $E_{\mathrm{Th}}∕\Delta =0.01$, and $\alpha ∕\pi =0.125$.