Proximity induced superconductivity in quasicrystal-superconductor hybrid rings

Quasicrystals with their exotic long range spatial order are expected to
host an exotic superconducting state. As a first step to
understanding these new kinds of superconducting systems, we
have studied proximity-induced superconductivity in a hybrid 1D chain. The
hybrid system is modeled using the Bogoliubov-de Gennes approach, consists of
a non-interacting Fibonacci chain coupled to a periodic superconductor. This
quasiperiodic chain has topological properties which have been explored in a
number of experimental/theoretical works. We show that an inhomogeneous
superconductivity is induced in the normal chain, and, in particular, how edge
states affect the induced pairing amplitudes.