The role of next nearest neighbor (NNN) hopping (t') and next to NNN hopping (t'') on hole pairing and thermodynamic properties such as specific heat, entropy have been investigated using two dimensional (2D) hole-doped t-t'-t''-J model based on exact diagonalization (ED) method. Standard Periodic boundary conditions are applied to minimize error due to finite size effect as the calculations are made using small sized cluster geometry. The attraction between holes increases with the inclusion of third neighbor hopping term. The maximum probability of hole pairing is at NNN site. The system goes to more disordered and ordered state with the increase of long range hopping terms at temperature T≤0.35t and T>0.35t, respectively. A single peak nature is observed in specific heat graph.
The attractive Hubbard model plays a paradigmatic role in the study of superconductivity (superfluidity) and has become directly realizable in ultracold atom experiments on optical lattices. However, the critical temperatures,
Tc's, remain lower than the lowest temperatures currently achievable in experiments. Here, we explore a possible route to enhance
Tc by introducing an additional next-nearest-neighbor (NNN) hopping,
t′, in a two-dimensional square lattice. We perform sign-problem-free determinant quantum Monte Carlo simulations to compute response functions such as pairing correlation functions, superfluid density, and uniform spin susceptibility. Our results show that a judicious choice of
t′ can increase
Tc by up to
50% compared to the case with only nearest-neighbor hopping. In contrast, the preformed pairs temperature scale, named pairing temperature,
Tp, decreases with increasing
∣t′/t∣, which should represent a reduction of the pseudogap region, favoring a more BCS-like behavior at intermediate coupling. We further analyze the interacting density of states to characterize the transition from a pseudogap regime to a fully gapped superconducting state. These findings suggest that NNN hopping could be a viable route to increase
Tc to values closer to experimentally accessible temperature scales.
To clarify the effects of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the spin, charge, and pairing correlations, we studied the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ Hubbard model using the constrained-path Monte Carlo technique. We found that a negative ${t}^{\ensuremath{'}}$ suppresses the spin fluctuations near the Brillouin zone point $M=(\ensuremath{\pi},\ensuremath{\pi})$ and the charge fluctuations near the point $X=(\ensuremath{\pi},0),$ while a positive ${t}^{\ensuremath{'}}$ has the opposite effect. For a negative ${t}^{\ensuremath{'}},$ we also found that the long-range vertex contributions to the pairing correlations are heavily suppressed, but the local contributions are enhanced. Over the entire hole doping range studied, the d-wave long-range vertex contributions to pairing dominated those of the extended s-wave vertex contributions. In general, we did not find any tendency for these correlations to grow with increasing system size. We also did a limited number of simulations with an attractive nearest neighbor density-density interaction added to the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ model. It enhanced the long-range vertex contributions to the pairing correlations only for weak values of U.