Competition between $d$-wave and $d$+$is$-wave superconductivity in the Hubbard model on a checkerboard lattice

TL;DR

This study uses determinant quantum Monte Carlo simulations to explore the competition between $d$-wave and $d+is$-wave superconductivity in a frustrated Hubbard model on a checkerboard lattice, revealing how electron interactions influence pairing symmetries.

Contribution

It provides the first detailed numerical analysis of pairing symmetry competition in the checkerboard lattice Hubbard model considering frustration effects.

Findings

Dominant pairing symmetry varies with electron filling and frustration parameter.

Superconducting tendencies are enhanced by increasing Coulomb interaction.

Spin susceptibility and pairing interactions grow stronger with electron-electron correlations.

Abstract

By employing determinant quantum Monte Carlo simulations, we investigate a checkerboard lattice with next-nearest-neighbor hopping $t'$ as the frustration-control parameter, which exhibits an energetically partial flat-band in the system. Our numerical simulation identifies the dominant pairing symmetry of the checkerboard lattice Hubbard model, and we reveal the competition between the $d$-wave and $d+is$ wave in the parameter space of electron filling $\avg{n}$ and frustration control parameter $t^{\prime}/t$. To ensure the reliability and accuracy of our results, we evaluate the sign problem. We also find that the spin susceptibility, the effective pairing interactions of different pairing symmetries and the superconducting instability are enhanced as the on-site Coulomb interaction increases, demonstrating that superconductivity is driven by strong electron--electron correlation. Our work provides a further understanding of pairing symmetry in the Hubbard model and improves prospects for exploring rich correlated behaviors in frustrated systems.