Superconductivity and Charge Density Wave in the Holstein Model on the Penrose Lattice

The exotic quantum states emerging in the quasicrystal (QC) have attracted extensive interest because of various properties absent in the crystal. In this Letter, we systematically study the Holstein model at half filling on a prototypical structure of QC, namely rhombic Penrose lattice, aiming at investigating the superconductivity (SC) and other intertwined ordering arising from the interplay between quasiperiodicity and electron-phonon interaction. Through unbiased sign-problem-free determinant quantum Monte Carlo simulations, we reveal the salient features of the ground state phase diagram. Distinct from the results on bipartite periodic lattices at half filling, SC is dominant in a large parameter regime of the electron-phonon coupling (EPC) strength on the Penrose lattice. The strongest SC emerges in the intermediate EPC strength regime, where it coexists with the charge density wave. The charge density wave dominates the SC only in the sufficiently strong EPC regime. Our results also reveal pronounced pairing fluctuation above the transition temperature T_{c} of the SC. The strong pairing and its fluctuation originate from the cooperative effects of the QC structure without translational symmetry and the macroscopically degenerate confined states at the Fermi energy, which uniquely exist on the Penrose lattice. Our unbiased numerical results suggest that the Penrose lattice is a potential platform to realize strong SC pairing, providing a promising avenue to discover relatively high-T_{c} SC predominantly induced by the EPC.