Intrinsic Superconductivity in Quasiperiodic Systems

The discovery of superconductivity in an Al-Zn-Mg quasicrystal by Kamiya et al. in 2018 has resulted in renewed efforts by the quasicrystal community to characterize the properties of superconducting phases in quasiperiodic materials. As a first step in that direction, we apply the Bogoliubov-de Gennes approach to the simplest quasicrystal, the Fibonacci Chain. We consider the hopping model in which the amplitudes can take two possible values t_A and t_B. We find that increasing the strength of the quasiperiodic modulation stabilizes the SC phase, in that the critical temperature T_c becomes larger with the difference of hopping amplitudes. We will show results for the local densities of states. We will report on how the superconducting gap and the resonant peaks evolve as a function of increasing interaction strength V. We will also discuss the spatial dependence of the local order parameters, as plotted in real space. As is well-known, the quasicrystal can be derived from a higher dimensional periodic system. We will use this property to show that the order parameter depends on the local environments in a simple and systematic way.