Supercurrent Distribution on Ammann-Beenker Structure

We study the distribution of supercurrent in the attractive Hubbard model on a periodic approximant of the Ammann-Beenker structure by means of the Bogoliubov-de Gennes (BdG) mean-field theory. We first investigate the spatial distributions of the electron density and superconducting order parameter and find a crossover between superconducting states with (i) extended, (ii) localized, and (iii) short-ranged Cooper pairs, similar to the previous results on the Penrose tiling. Furthermore, we formulate the expression of the supercurrent for the periodic approximant in terms of the eigenenergies and the wave functions of the Bogoliubov-de Gennes Hamiltonian and numerically investigate how the local supercurrent distribution varies by changing the direction of the applied phase gradient.