The proximity effect in disordered and quasiperiodic systems

We investigate the superconducting proximity effect in one-dimensional hybrid rings with a superconducting and a normal part. We consider two cases: when the normal part is a) a weakly disordered crystal and b) quasiperiodic. We carry out self-consistent calculations using a real space mean field Bogoliubov-de Gennes type approach within the tight binding framework. For the disordered case we find that the decay of the superconducting order parameter into the normal region reflects the the band center anomaly—a cusp like deformation in the density of states around E=0 known to exist for weak disorder. The order parameter decay when the normal chain has a Fibonacci hopping sequence will be discussed as well, along with the key features that differentiate the proximity effect in the two cases.