Resonant peak in the density of states in normal-metal/diffusive-ferromagnet/superconductor junctions

The conditions for the formation of zero-energy peak in the density of states (DOS) in the normal metal/insulator/diffusive $\text{ferromagnet}∕\text{insulator}∕s$-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel equations. The DOS of the diffusive-ferromagnet conductor (DF) is calculated in various regimes for different magnitudes of the resistance, Thouless energy, and the exchange field of the DF, as well as for various resistances of the insulating barriers. The conditions for the DOS peak are formulated for the cases of weak proximity effect [large resistance of the diffusive-feromagnet/superconductor (DF/S) interface] and strong proximity effect (small resistance of the DF/S interface).

Figure 1

Normalized zero energy DOS as a function of $E_{\mathit{Th}}$ for large resistance of the N/DF interface $R_d∕R_b^{\prime }=0.1$ and various $h∕\Delta$ with resistance ratios at the DF/S interface (a) $R_d∕R_b=1$, (b) $R_d∕R_b=5$, and (c) $R_d∕R_b=10$.

Figure 2

Normalized DOS as a function of $\epsilon$ for $R_d∕R_b^{\prime }=0.1$ and various $h∕\Delta$ with (a) $R_d∕R_b=1$ and $E_{\mathit{Th}}=2h{R}_b∕R_d=2h$, (b) $R_d∕R_b=5$ and $E_{\mathit{Th}}=h$, and (c) $R_d∕R_b=10$ and $E_{\mathit{Th}}=h$.

Figure 3

Normalized DOS at zero energy as a function of $E_{\mathit{Th}}$ for $h∕\Delta =1$ and various $R_d∕R_b^{\prime }$ with (a) $R_d∕R_b=5$ and (b) $R_d∕R_b=10$.

Figure 4

Spatial dependence of $\mathrm{Im}\theta$ for majority spin for $R_d∕R_b^{\prime }=0.1$, $E_{\mathit{Th}}∕\Delta =1$ and various $h∕\Delta$ with (a) $R_d∕R_b=5$ and (b) $R_d∕R_b=10$. The DF/N interface and the DF/S interface are located at $x=0$ and $x=L$ respectively.