Resonant proximity effect in normal metal/diffusive ferromagnet/superconductor junctions

Resonant proximity effect in the normal metal/insulator/diffusive ferromagnet/insulator/$s$- wave and $d$-wave superconductor (N/I/DF/I/S) junctions is studied for various regimes by solving the Usadel equation with the generalized boundary conditions. Conductance of the junction and the density of states in the DF layer are calculated as a function of the insulating barrier heights at the interfaces, the magnitudes of the resistance, Thouless energy, and the exchange field in DF, and the misorientation angle $\alpha$ of a $d$-wave superconductor. It is shown that the resonant proximity effect originating from the exchange field in the DF layer strongly modifies the tunneling conductance and density of states. We have found that, due to the resonant proximity effect, for $s$-wave junctions a sharp zero bias conductance peak (ZBCP) appears for small Thouless energy, while a broad ZBCP appears for large Thouless energy. The magnitude of this ZBCP can exceed the normal state conductance in contrast to the case of diffusive normal metal/superconductor junctions. Similar structures exist in the density of states in the DF layer. For $d$-wave junctions at $\alpha =0$, similar structures are predicted in the conductance and the density of states. With the increase of the angle $\alpha$, the magnitude of the resonant ZBCP decreases due to the formation of the midgap Andreev resonant states.

Figure 1

(Color online) Normalized tunneling conductance for $s$-wave superconductors with $R_d∕R_b=1$ and $E_{Th}∕\Delta =0.01$.

Figure 2

(Color online) Normalized DOS for $s$-wave superconductors with $Z=3$, $R_d∕R_b=1$, and $E_{Th}∕\Delta =0.01$.

Figure 3

(Color online) Normalized tunneling conductance for $s$-wave superconductors with $R_d∕R_b=5$ and $E_{Th}∕\Delta =0.01$.

Figure 4

(Color online) Normalized DOS for $s$-wave superconductors with $Z=3$, $R_d∕R_b=5$ and $E_{Th}∕\Delta =0.01$.

Figure 5

(Color online) Normalized tunneling conductance and corresponding DOS for $s$-wave superconductors with $Z=3$, $R_d∕R_b=1$, and $E_{Th}∕\Delta =10$.

Figure 6

(Color online) Normalized tunneling conductance and corresponding DOS for $s$-wave superconductors with $Z=3$, $R_d∕R_b=5$, and $E_{Th}∕\Delta =10$.

Figure 7

(Color online) Spatial dependence of $\mathrm{Re}\theta$ and $\mathrm{Im}\theta$ for $s$-wave superconductors with $Z=3$, $E_{Th}∕\Delta =0.01$. $R_d∕R_b=1$ (left panels) and $R_d∕R_b=5$ (right panels).

Figure 8

(Color online) Normalized tunneling conductance for $d$-wave superconductors with $Z=3$ and $R_d∕R_b=1$.

Figure 9

(Color online) Normalized DOS for $d$-wave superconductors with $Z=3$, $R_d∕R_b=1$, $E_{Th}∕\Delta =10$, and $h∕\Delta =5$. (a) $\alpha ∕\pi =0$ and (b) $\alpha ∕\pi =0.125$.

Figure 10

(Color online) Normalized tunneling conductance for $d$-wave superconductors with $Z=3$ and $R_d∕R_b=5$.

Figure 11

(Color online) Normalized DOS for $d$-wave superconductors with $Z=3$, $R_d∕R_b=5$, $E_{Th}∕\Delta =10$, and $h∕\Delta =10$. (a) $\alpha ∕\pi =0$ and (b) $\alpha ∕\pi =0.125$.