本文通过自洽求解 Keldysh-Usadel 方程研究正常金属/超导体/正常金属结构，证明在反近邻效应较弱、界面电阻和超导区长度合适时 CAR 可压倒 EC，并分析自旋劈裂与自旋选择偏置的调控作用。
摘要：
交叉 Andreev 反射（CAR）是一种在空间分离的电子与空穴之间产生纠缠的过程。这类纠缠对在量子信息处理中具有潜在应用，因此确定如何提高 CAR 的概率具有现实意义。CAR 与另一种称为弹性共隧穿（EC）的非局域过程相互竞争，而后者不会产生纠缠。在传统的正常金属/超导体/正常金属异质结构中，早期理论工作预测 EC 相对于 CAR 占主导。然而，我们通过数值计算表明，当在超导体中自洽求解 Keldysh-Usadel 方程时，CAR 可以压倒 EC。自洽性对于准粒子电流到超流的转换以及正确描述序参量的空间变化都是必要的。CAR 概率超过 EC 概率的一个条件是反近邻效应较小。否则，亚电压态密度会变大，并且流过超导体的准粒子会增强 EC。因此，随着界面电阻和超导区域长度的增加，CAR 在非局域输运中占据主导。我们的结果表明，即便是采用容易获得的正常金属和超导体构成的最简单实验装置，也可以通过正确设计实验参数来获得占主导的 CAR。我们还发现，超导体中的自旋劈裂会提高亚电压态密度，从而总是更有利于 EC 而非 CAR。最后，我们调节引线中的化学势，使输运由一种自旋类型的电子主导。与使用自旋简并电压偏置相比，这可以在有限自旋劈裂值下提高 CAR 概率，并提供一种电学控制传导电子自旋的方法。
英文摘要：
Crossed Andreev reflection (CAR) is a process that creates entanglement between spatially separated electrons and holes. Such entangled pairs have potential applications in quantum information processing, and it is therefore relevant to determine how the probability for CAR can be increased. CAR competes with another non-local process called elastic cotunneling (EC), which does not create entanglement. In conventional normal metal/superconductor/normal metal heterostructures, earlier theoretical work predicted that EC dominates over CAR. Nevertheless, we show numerically that when the Keldysh-Usadel equations are solved self-consistently in the superconductor, CAR can dominate over EC. Self-consistency is necessary both for the conversion from a quasiparticle current to a supercurrent and to describe the spatial variation of the order parameter correctly. A requirement for the CAR probability to surpass the EC probability is that the inverse proximity effect is small. Otherwise, the subvoltage density of states becomes large and EC is strengthened by quasiparticles flowing through the superconductor. Therefore, CAR becomes dominant in the non-local transport with increasing interface resistance and length of the superconducting region. Our results show that even the simplest possible experimental setup with easily accessible normal metals and superconductors can provide dominant CAR by designing the experimental parameters correctly. We also find that spin-splitting in the superconductor increases the subvoltage density of states, and thus always favors EC over CAR. Finally, we tune the chemical potential in the leads such that transport is governed by electrons of one spin type. This can increase the CAR probability at finite values of the spin-splitting compared to using a spin-degenerate voltage bias, and provides a way to control the spin of the conduction electrons electrically.
