# Optimal inhomogeneity for pairing in Hubbard systems with next-nearest-neighbor hopping

## TL;DR

This study investigates how inhomogeneous hopping in Hubbard systems with complex band structures affects pairing, revealing optimal inhomogeneity levels and the influence of next-nearest-neighbor hopping on pairing strength.

## Contribution

It extends previous work by analyzing inhomogeneous hopping effects in Hubbard models with next-nearest-neighbor interactions using exact diagonalization and DMRG methods.

## Key findings

- Optimal inhomogeneity enhances pairing at intermediate levels.
- Positive t_d/t increases pair-binding energy, negative t_d/t suppresses it.
- Pairing correlates with magnetic properties of the system.

## Abstract

Previous studies have shown that bipartite Hubbard systems with inhomogeneous hopping amplitudes can exhibit higher pair-binding energies than the uniform model. Here we examine whether this result holds for systems with a more generic band structure. To this end, we use exact diagonalization and the density matrix renormalization group method to study the 4x4 Hubbard cluster and the two-leg Hubbard ladder with checkerboard-modulated nearest-neighbor hopping, t, and next-nearest-neighbor (diagonal) hopping, t_d. We find that the strongest pairing continues to occur at an intermediate level of inhomogeneity. While the maximal pair-binding energy is enhanced by a positive t_d/t, it is suppressed and appears at weaker repulsion strengths and smaller hole concentrations when t_d/t is negative. We point out a possible connection between the pairing maximum and the magnetic properties of the system.