We show experimentally that in nanometer scaled superconductor/normal metal hybrid devices and in a small window of contact resistances, crossed Andreev reflection (CAR) can dominate the nonlocal transport for all energies below the superconducting gap. Besides crossed Andreev reflection, elastic cotunneling (EC) and nonlocal charge imbalance can be identified as competing subgap transport mechanisms in temperature dependent four-terminal nonlocal measurements. We demonstrate a systematic change of the nonlocal resistance vs. bias characteristics with increasing contact resistances, which can be varied in the fabrication process. For samples with higher contact resistances, CAR is weakened relative to EC in the midgap regime, possibly due to dynamical Coulomb blockade. Gaining control of crossed Andreev reflection is an important step towards the realization of a solid state entangler.Quantum mechanically entangled pairs of particles are a major building block of quantum computation and information processing. A natural source of entangled electrons is a BCS-type superconductor where the Cooper pairs (CP) form spin singlet states. The two electrons of a Cooper pair can be spatially separated into two different metallic leads in a nonlocal process called crossed Andreev reflection (CAR) [1, 2, 3,4].At temperatures (T ) well below the superconducting transition temperature, T c , and for bias potentials below the superconducting energy gap ∆, electrons from a normal metal contact (N) can enter the superconductor (S) only as Cooper pairs by a process known as Andreev reflection (AR). In this local process a hole is reflected into the same N to conserve momentum. If two normal metal contacts, N1 and N2, are spatially separated by less than the coherence length ξ, the two electrons forming a CP can originate from different normal contacts, see Fig. 1(a). This process opens an additional nonlocal conduction path known as CAR. An inverse process was proposed as the basis of a solid-state entangler: the electrons of a CP are split between the two leads while retaining their entanglement from the superconductor. However, this method of creating entangled particles can be accompanied by two additional processes that lead to correlated signals on N1 and N2, but not to entanglement. In the first, a single electron from N1 can reach the other contact N2 by elastic cotunneling (EC) [5, 6,7], see Fig. 1(b). In the second, called nonlocal charge imbalance (CI), electrical charge can be transferred to the second contact by the diffusion of quasi-particles generated by finite temperatures or finite bias.Recently, the relative strength of these subgap processes was the subject of extensive theoretical work. Standard BCS theory predicts that to lowest order in the tunneling rates, CAR and EC exactly cancel in normal metal/insulator/superconductor (NIS) systems at low T and bias [6]. This cancelation can be lifted for higher transmissions [8], by spin-active interfaces [9] or ferromagnetic contacts [7], by disorder, or by electron-e...
Crossed Andreev reflection (CAR) in metallic nanostructures, a possible basis for solid-state electron entangler devices, is usually investigated by detecting non-local voltages in multi-terminal superconductor/normal metal devices. This task is difficult because other subgap processes may mask the effects of CAR. One of these processes is the generation of charge imbalance (CI) and the diffusion of non-equilibrium quasi-particles in the superconductor. Here we demonstrate a characteristic dependence of non-local CI on a magnetic field applied parallel to the superconducting wire, which can be understood by a generalization of the standard description of CI to non-local experiments. These results can be used to distinguish CAR and CI and to extract CI relaxation times in superconducting nanostructures. In addition, we investigate the dependence of non-local CI on the resistance of the injector and detector contacts and demonstrate a quantitative agreement with a recent theory using only material and junction characteristics extracted from separate direct measurements.
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