Crossed Andreev reflection at spin-active interfaces

With the aid of the quasiclassical Eilenberger formalism we develop a theory of nonlocal electron transport across three-terminal ballistic normal-superconducting-normal (NSN) devices with spin-active NS interfaces. The phenomenon of crossed Andreev reflection (CAR) is known to play the key role in such transport. We demonstrate that CAR is highly sensitive to electron spins and yields a rich variety of properties of nonlocal conductance which we describe nonperturbatively at arbitrary voltages, temperature, spin-dependent interface transmissions, and their polarizations. Our results can be applied to multiterminal hybrid structures with normal, ferromagnetic, and half-metallic electrodes and can be directly tested in future experiments.

Figure 1

Two elementary processes contributing to nonlocal conductance of an NSN device: (1) direct electron transfer and (2) crossed Andreev reflection.

Figure 2

Schematics of our NSN device.

Figure 3

Riccati amplitudes for incoming and outgoing trajectories from both sides of the interface.

Figure 4

Riccati amplitudes for incoming and outgoing trajectories for an NSN structure with two barriers. The arrows define quasiparticle momentum directions. We also indicate relevant Riccati amplitudes and distribution functions parametrizing the Green-Keldysh function for the corresponding trajectory.

Figure 5

Diagrams representing four different contributions to the cross-current $I_{12}$ [Eq. (64)]. Solid (dotted) lines correspond to propagating electronlike (holelike) excitations and $t_{21}=K_{21}^{-1}∕\cosh (iL\Omega ∕v_F)$.

Figure 6

(Color online) Zero temperature differential nonlocal conductance as a function of voltage at zero spin-mixing angles ${\theta }_{1,2}=0$.

Figure 7

(Color online) The same as in Fig. 6 for ${\theta }_1=\pi ∕2$, ${\theta }_2=\pi ∕4$.