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

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 $4\ifmmode\times\else\texttimes\fi{}4$ 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 lower 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.