Correlated tunneling into a superconductor in a multiprobe hybrid structure

We consider tunneling in a hybrid system consisting of a superconductor with two or more probe electrodes which can be either normal metals or polarized ferromagnets. In particular we study transport at subgap voltages and temperatures. Besides Andreev pair tunneling at each contact, in multi-probe structures subgap transport involves additional channels, which are due to coherent propagation of two particles (electrons or holes), each originating from a different probe electrode. The relevant processes are electron cotunneling through the superconductor and conversion into a Cooper pair of two electrons stemming from different probes. These processes are non-local and decay when the distance between the pair of involved contacts is larger than the superconducting coherence length. The conductance matrix of a three-terminal hybrid structure is calculated. The multi-probe processes enhance the conductance of each contact. If the contacts are magnetically polarized the contribution of the various conduction channels can be separately detected.