Signatures of retroreflection and induced triplet electron-hole correlations in ferromagnet–$s$-wave-superconductor structures

We present a theoretical study of a ferromagnet–$s$-wave-superconductor junction to investigate the signatures of induced triplet correlations in the system. We apply the extended Blonder-Tinkham-Klapwijk formalism and allow for an arbitrary magnetization strength and direction of the ferromagnet, a spin-active barrier, Fermi-vector mismatch, and different effective masses in the two systems. It is found that the phase associated with the $xy$ components of the magnetization in the ferromagnet couples with the superconducting phase and induces spin triplet pairing correlations in the superconductor, if the tunneling barrier acts as a spin filter. This feature leads to an induced spin-triplet pairing correlation in the ferromagnet, along with a spin-triplet electron-hole coherence due to an interplay between the ferromagnetic and superconducting phases. As our main result, we investigate the experimental signatures of retrorelection, manifested in the tunneling conductance of a ferromagnet–$s$-wave-superconductor junction with a spin-active interface.

Figure 1

(Color online) Schematic overview of the relevant scattering processes that take place at the F/S interface. We take into account the possibility of retroreflected holes with equal spin as the incoming electron. This is due to the presence of spin-flip processes manifested in the form of planar magnetization and a spin-active barrier.

Figure 2

(Color online) Plot of the probability coefficients associated with the scattering processes at the interface. For an electron with incoming spin $\sigma$, the green (dash-dotted) line corresponds to normal reflection with spin $\sigma$, the magenta (dashed) line corresponds to Andreev-reflection of a hole with spin $-\sigma$, and the blue (solid) line designates reflection without branch crossing with spin $-\sigma$, while the presence of retroreflection—i.e., Andreev reflection of a hole with spin $\sigma$—is indicated by the red (dotted) line. Note from (d) that in order to get retroreflection, both an in-plane magnetization and a spin-active barrier are required.

Figure 3

(Color online) Plot of probability coefficients for $Z=1$ and $R_V=0.95$ in the absence of any net polarization for several values of $M_{xy}$. It is seen that for increasing $M_{xy}$—i.e., larger effect of spin-flip scattering—the retroreflection process dominates the “normal” Andreev reflection.

Figure 4

(Color online) Conductance spectrum for weak spin-flip scattering $(M_{xy}=0.1E_F)$ and $M_z=0$ with $R_V=0.5$ for several values of $Z$.

Figure 5

(Color online) Conductance spectrum for strong spin-flip scattering $(M_{xy}=0.5E_F)$ and $M_z=0$ with a strongly spin-dependent barrier $(R_V=0.95)$ for several values of $Z$.

Figure 6

(Color online) Conductance spectrum for zero spin-flip scattering and purely nonmagnetic scattering potential (upper panel), spin-flip scattering and purely nonmagnetic scattering potential (middle panel), and spin-flip scattering and mixed magnetic and nonmagnetic scattering potential (lower panel). For all panels, $M_z∕E_F=0.866$ for comparison with Ref. 18. The lines are given at $E=1.4$ for the upper panel as follows (from top to bottom): $R_E=\{1,1∕\sqrt{2},1∕2,1∕4,1∕9,1∕16\}$.

Figure 7

(Color online) Conductance spectra for various nonmagnetic scattering potentials upon varying the polarization of the ferromagnet with $M_{xy}=0.1E_F$ and $R_V=0.5$.

Figure 8

(Color online) Conductance spectra for various nonmagnetic scattering potentials upon varying the polarization of the ferromagnet with $M_{xy}=0.5E_F$ and $R_V=0.95$.

Figure 9

(Color online) Conductance spectra for different effective masses with parameters $M_{xy}=0.1E_F$ and $R_V=0.5$.

Figure 10

(Color online) Conductance spectra for different effective masses with parameters $M_{xy}=0.5E_F$ and $R_V=0.95$.

Figure 11

(Color online) Conductance spectra in the presence of retroreflection but in the absence of any net polarization. Here, $M_{xy}=0.5E_F$ while $M_Z=0$.

Figure 12

(Color online) Conductance spectra in the presence of retroreflection and a net polarization. Here, $M_{xy}=0.5E_F$ while $M_Z=0.5E_F$.

Figure 13

(Color online) In the limit $M_{xy}\to 0$, the formation of a ZBCP is observed with decreasing $R_E$. This illustrates how the effect of Fermi-vector mismatch may “mimick” the usual signature of unconventional superconductivity—namely, the appearance of a ZBCP for certain crystal orientations. This was first discussed in Ref. 18, see their Fig. 3. From top to bottom, the curves correspond to the following pairs of $(R_E,M_z∕E_F)$: $(1,0)$, $(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$, $(\frac{1}{2},0.866)$, $(\frac{1}{4},0.968)$, $(\frac{1}{9},0.994)$, and $(\frac{1}{16},0.998)$.