Increasing superconducting $T_c$ by layering in the attractive Hubbard model

TL;DR

This study demonstrates that layering in the attractive Hubbard model can significantly increase the superconducting transition temperature, with bilayer and cubic lattice configurations showing notable enhancements over single layers.

Contribution

The paper introduces layering strategies in the attractive Hubbard model to boost $T_c$, supported by quantum Monte Carlo simulations and analysis of physical response functions.

Findings

Bilayer can have $T_c$ 1.5 to 1.7 times higher than single layer.

Simple cubic lattice shows about 30% $T_c$ increase over single layer.

Validation of BCS estimate and superfluid density bounds for $T_c$.

Abstract

The attractive Hubbard model has become a model readily realizable with ultracold atoms on optical lattices. However, the superconducting (superfluid) critical temperatures, $T_c$'s, are still somewhat smaller than the lowest temperatures achieved in experiments. Here we consider two possible routes, generically called layering, to increase $T_c$: a bilayer and a simple cubic lattice, both with tunable hopping, $t_z$, between attractive Hubbard planes. We have performed minus-sign--free determinant quantum Monte Carlo simulations to calculate response functions such as pairing correlation functions, uniform spin susceptibility, and double occupancy, through which we map out some physical properties. We have found that by a judicious choice of fillings and intensity of on-site attraction, a bilayer can exhibit $T_c$'s between 1.5 and 1.7 times those of the single layer; for the simple-cubic lattice the enhancement can be 30\% larger than the maximum for the single layer. We also check the accuracy of both a BCS-like estimate for $T_c$ in the attractive Hubbard model, as well as of an upper bound for $T_c$ based on the superfluid density.