Dr. Arne Brataas
Norwegian University of Science and Technology

Circuit Theory of Crossed Andreev Reflection

In crossed Andreev reflection two electrons from spatially separated normal conductors enter a superconductor as a Cooper pair. This can result in the production of spatially separated entangled electrons. We consider effects of crossed Andreev reflection in two set-ups: i) non-local conductance in a three terminal device with one superconducting and two normal metals and ii) the production of spatially entangled electrons in ferromagnetic leads from Cooper pairs in a superconducting lead. For the first system, the nonlocal conductance is given by competing contributions from crossed Andreev reflection and electron cotunneling, and we determine the contribution from each process. The nonlocal conductance vanishes when there is no resistance between the superconducting terminal and the device, in agreement with previous theoretical work. Electron cotunneling dominates when there is a finite resistance between the device and the superconducting reservoir. Decoherence is taken into account, and the characteristic timescale is the particle dwell time. Both the conductance due to crossed Andreev reflection and electron cotunneling depend strongly on the particle dwell time. For the second, spin-polarized device, we give a complete description of the elementary charge transfer processes, i) transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasiparticles among the ferromagnetic leads, in terms of their statistics. The probabilities that entangled electrons flow into spatially separated leads aredetermined by experimentally measurable conductances and polarizations. Finally, we investigate how currents, noise and cross correlations are affected by transport of entangled electrons.