Superconductivity in the Fibonacci Chain

The discovery of superconductivity in Al–Zn–Mg quasicrystal paved the way for fractal superconductivity[1]. We consider approximants of the Fibonacci chain, which are periodic structures locally retaining quasiperiodic character inside a large unit cell. For a fixed unit cell size, our model is characterized by the quasiperiodic modulation strength. Superconductivity is introduced by an attractive Hubbard interaction. We apply the Bogoliubov-de Gennes mean field theory for the simulation. We find that sites with similar local environments have order parameters of similar magnitude, regardless of the distance between them. The multifractality of the spectrum results in a rich phase diagram as a function of doping and pairing strength. The superconducting gap is insensitive to fluctuations in the local order parameter. This is a corollary to the fact that the entire length of the quasicrystal has the same critical temperature. The critical temperature increases quadratically with the modulation strength. These findings are of interest to the application of low-dimensional quasicrystals.

[1] K. Kamiya, T. Takeuchi, N. Kabeya, N. Wada, T. Ishimasa, A. Ochiai, K. Deguchi, K. Imura, and N. K. Sato, Nature Communications 9, 154 (2018)