Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice

TL;DR

This study uses quantum Monte Carlo simulations to explore how quasiperiodic Penrose lattices influence superconductivity and charge-density waves in the Holstein model, revealing unique ground states and potential for high-temperature superconductivity.

Contribution

First systematic investigation of the Holstein model on a Penrose lattice showing dominant superconductivity and its suppression by charge-density waves, highlighting the role of quasiperiodicity.

Findings

Superconductivity is dominant over a large parameter regime on the Penrose lattice.

Charge-density-wave order appears at strong electron-phonon coupling, suppressing superconductivity.

Strong pairing fluctuations exist above the superconducting transition temperature.

Abstract

The exotic quantum states emerging in the quasicrystal (QC) have attracted extensive interest because of various properties absent in the crystal. In this paper, 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 ({\it e}-ph) 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 on the Penrose lattice. When {\it e}-ph coupling is sufficiently strong, charge-density-wave order appears and strongly suppresses the SC. The strongest SC emerges at intermediate {\it e}-ph coupling strength and pronounced pairing fluctuation exists above the SC transition temperature. The strong pairing originates from the cooperative effects of unique lattice structure and macroscopically degenerate confined states at Fermi energy which uniquely exist on the Penrose lattice. Moreover, we demonstrate the forbidden ladders substantially suppress the phase coherence of SC. Our unbiased numerical results suggest that Penrose lattice is a potential platform to realize strong SC pairing, providing a promising avenue to searching for relatively high-$T_c$ SC dominantly induced by {\it e}-ph coupling.