Detection of non separable correlations with dc transport: a new type of Aharonov-Bohm effect

Abstract

I construct a minimal formalism to describe transport of non separable correlations arising when a superconductor is in contact with several electrodes (being ferromagnetic or normal metal). Transport theory is expressed in terms of effective single site Green's functions. Part of the circuit is decimated exactly by renormalizing only one physical parameter (the density of states). I show that the physical current is obtained by acting on the infinite series of Feynman diagrams with an operator counting the charge of a given diagram. I use this method to propose a new Aharonov-Bohm experiment intended to detect non separable correlations. In this experiment, spin-$σ$ electrons are forced to travel around an Aharonov-Bohm loop in the presence of an applied magnetic flux, while spin-($- σ$) electrons are not directly coupled to the magnetic flux. It is shown that the spin-($-σ$) current oscillates as a function of the flux to which spin-$σ$ electrons are coupled. It is predicted that the effect exists both with high and low transparency contacts, and that the electrodes can be normal metal in which phase coherence can propagate over large distances. Three other aspects of the problem are investigated: (i) The dependence of the superconducting gap on spin polarization of ferromagnetic electrodes connected to the superconductor; (ii) The detection of linear superposition of correlated pairs of electrons; (iii) The proximity effect version of cryptomagnetism.