d-Wave superconductivity on the checkerboard Hubbard model at weak and strong coupling

TL;DR

This study investigates how inhomogeneity affects d-wave superconductivity in the checkerboard Hubbard model across different coupling regimes, revealing suppression in weak coupling and monotonic decrease in strong coupling, with implications for high-Tc materials.

Contribution

It provides a comprehensive analysis of inhomogeneity effects on d-wave superconductivity in the checkerboard Hubbard model at both weak and strong coupling regimes.

Findings

In weak coupling, inhomogeneity suppresses the order parameter at low to intermediate doping.

In strong coupling, inhomogeneity monotonically decreases the superconducting order parameter.

A first-order transition from superconducting to normal state occurs at high inhomogeneity in the underdoped regime.

Abstract

It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the height of the coherence peaks and hence is an appropriate measure of the strength of superconductivity. The weak coupling results reveal a suppression of the order parameter in the presence of inhomogeneity for small to intermediate hole dopings, while it is enhanced for large dopings. In contrast, for strong coupling there is a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity over the entire doping range of interest. Furthermore, at moderately high inhomogeneity, the system undergoes a first-order transition from the superconducting to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the superconducting order parameter correlates with the height of the lowest energy peak in the spectral weight of antiferromagnetic spin fluctuations, confirming the connection between antiferromagnetic fluctuations and d-wave superconductivity found in earlier studies on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder.