Effect of Fibonacci modulation on superconductivity.

We have studied finite-sized single band models with short-range pairing interactions between electrons in the presence of diagonal Fibonacci modulation in one dimension. Two models, namely the attractive Hubbard model and the Penson-Kolb model, have been investigated at half-filling at zero temperature by solving the Bogoliubov-de Gennes equations in real space within a mean-field approximation. The competition between 'disorder' and the pairing interaction leads to a suppression of superconductivity (of usual pairs with zero centre-of-mass momenta) in the strong-coupling limit while an enhancement of the pairing correlation is observed in the weak-coupling regime for both models. However, the dissimilarity of the pairing mechanisms in these two models brings about notable differences in the results. The extent to which the bond-ordered wave and the η-paired (of pairs with centre-of-mass momenta = π) phases of the Penson-Kolb model are affected by the disorder has also been studied in the present calculation. Some finite size effects are also identified.