Inhomogeneous Hubbard Models: from Weak to Strong Coupling

Thomas Gerisch, Alfred Rieckers

Wei-Feng Tsai

Shiladitya Chakraborty, David Sénéchal, A.–M. S. Tremblay

It has been argued that inhomogeneity generally can enhance superconductivity (SC) in the cuprate high-${T}_{c}$ materials. To check the validity of this claim, we study $d$-wave SC 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 SC. 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 SC 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 SC to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the SC 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 SC found in earlier papers on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder.

Astrid Tranum Rømer, Thomas Maier, Andreas Kreisel +3 more

The authors present a comprehensive study of superconducting pairing in the one-band Hubbard model. By comparing different theoretical techniques, the paper shows that the hierarchy of pairing instabilities evolves smoothly from weak- to strong coupling. Additionally, the doping-dependence of the leading superconducting instability is mapped out, and found to be in agreement with previous theoretical studies of the one-band Hubbard model.

Vijay B. Shenoy

S. Pairault, David Sénéchal, A.–M. S. Tremblay