Effects of next-nearest neighbor hopping on the pairing and critical temperatures of the attractive Hubbard model on a square lattice

Abstract

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, $T_c$'s, remain lower than the lowest temperatures currently achievable in experiments. Here, we explore a possible route to enhance $T_c$ by introducing an additional next-nearest-neighbor (NNN) hopping, $t^\prime$, 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 $t^\prime$ 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, $T_p$, decreases with increasing $|t^{\prime}/t|$, 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 $T_c$ to values closer to experimentally accessible temperature scales.

Figures (12)

• Figure 1: Non-interacting density of states as a for $t^{\prime} = 0$ and $t^{\prime} = -0.2t$. The vertical lines locate the corresponding Fermi energies for $\langle n\rangle=0.87$. The inset shows the electronic density at which the van Hove singularity occurs, $n_{\hbox{vHS}}$, as a function of $t^{\prime} /t$.
• Figure 2: Band dispersion, Eq. \ref{['eq:ek']} for (a) $t'/t = 0.0$ and (b) $t'/t = -0.2$. The gray planes locate the Fermi energy for $\langle n \rangle = 0.87$.
• Figure 3: Typical portion of a square lattice illustrating the model parameters. Two fermions with opposite spins on the same site contribute with $-|U|$ to the total energy. Fermions hopping between nearest-neighboring sites (horizontally, $\hat{\mathbf{x}}$, or vertically, $\hat{\mathbf{y}}$) contribute with $-t$ (full lines) to the total energy. Fermions hopping along the diagonals, $\hat{\mathbf{x}}\pm\hat{\mathbf{y}}$, contribute with $-t'$ (dashed lines) to the total energy.
• Figure 4: Linear-log plots of the bare electronic susceptibilities for (a) the particle-hole and (b) the particle-particle channels as functions of temperature, and for several values of $t'$.
• Figure 5: CDW (empty symbols) and $s$-wave pairing (s) (filled symbols) structure factors as functions of $|t'/t|$, normalized to their values at $t'=0$. Data correspond to half filling, fixed $U=-5.0t$ and $\beta t = 20$, and linear lattice sizes $L=12$ (triangles) and $14$ (squares).