Statistical correlation for a three-terminal normal-metal–superconductor– superconductor hybrid system

Abstract

It is well known that the particles in a beam of bosons obeying Bose-Einstein statistics tend to cluster (bunching effect), while the particles in a degenerate beam of fermions obeying Fermi-Dirac statistics expel each other (antibunching effect). Here we investigate the statistical correlation effect for a three-terminal normal-metal–superconductor–superconductor hybrid mesoscopic system. By using a nonequilibrium Green’s-function technique, we obtain a positive cross correlation when the external voltage is smaller than the gap energy, which demonstrates bosonic behavior. In the larger voltage limit, the cross correlation becomes negative due to the contribution of the quasiparticles. At large voltages, the oscillation between fermionic and bosonic behavior of cross correlation is also observed in the strong-coupling regime as one changes the position of the resonant levels.