Nonlocal Andreev reflection at high transmissions

We analyze nonlocal effects in electron transport across three-terminal normal-superconducting-normal (NSN) structures. Subgap electrons entering the $S$ electrode from one $N$ metal may form Cooper pairs with their counterparts penetrating from another $N$ metal. This phenomenon of crossed Andreev reflection—combined with normal scattering at SN interfaces—yields two different contributions to nonlocal conductance which we evaluate nonperturbatively at arbitrary interface transmissions. Both these contributions reach their maximum values at fully transmitting interfaces and demonstrate interesting features which can be 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

Quasiclassical trajectories contributing to local (a) and nonlocal [(b) and (c)] currents.

Figure 4

(Color online) Differential nonlocal conductance at $T=0$ as a function of voltage for $D_1=0.5$, $D_2=0.8$, and different $L$. Inset: the same for $eV<\Delta$.