Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems

We study the superconducting proximity effect in a hybrid system, where the superconducting part is homogeneous and the non-superconducting part is either disordered, modelled by the off-diagonal Anderson Hamiltonian, or quasicrystalline, modeled by a Fibonacci tight-binding Hamiltonian. We find that when the wave functions are extended, as in the case of weak disorder, or critical, as in the quasicrystal, the pair amplitude at zero temperature spatially decays as a power law away from the interface. In the case of strong disorder, where wave functions are localized, the pair amplitude decays exponentially. In this respect, the quasicrystal has more in common with homogeneous systems than with disordered systems. However, if we consider fluctuations in the induced order parameter by studying the form of its distribution, the quasicrystal behaves more like a strongly disordered system. Furthermore, we demonstrate that the real space profile of the pair correlations in the quasicrystal exhibits two typical features seen in quasi-periodic systems: self-similarity, and enhancement or suppression around sites with high local symmetry depending on the Fermi level.