Superconductivity in bilayer $t$-$t'$ Hubbard models

TL;DR

This study uses variational Monte Carlo simulations on a bilayer $t$-$t'$ Hubbard model to investigate the effects of adjacent layers on superconductivity, finding that layers do not significantly enhance the optimal transition temperature.

Contribution

It provides evidence that adjacent layers in bilayer cuprates do not contribute to increased $T_c^{ m opt}$, challenging previous assumptions about layer effects on superconductivity.

Findings

Superconducting correlations are not enhanced in bilayer compared to single-layer models.

Superconducting correlations are smaller in the overdoped region due to van Hove singularity.

Amplitude of the superconducting gap functions is similar in single-layer and bilayer models at optimal doping.

Abstract

The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-$T_{\rm c}$ superconductors. In particular, the relationship between the number $n$ of CuO$_2$ layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature $T_{\rm c}^{\rm opt}$ is intriguing. As experimentally observed in layered cuprates, $T_{\rm c}^{\rm opt}$ increases when $n$ is increased, up to $n=3$, and, then, decreases for larger $n$. However, the mechanism behind the $n$ dependence of $T_{\rm c}^{\rm opt}$ remains elusive although there have been many studies on the $n$ dependence. In this paper, we studied a bilayer $t$-$t'$ Hubbard model to clarify the effects of the adjacent CuO$_2$ layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with $T_{\rm c}^{\rm opt}$. It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer $t$-$t'$ Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer $t$-$t'$ Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of $T_{\rm c}^{\rm opt}$ in the bilayer cuprates. Possible origins of the enhanced $T_{\rm c}^{\rm opt}$ other than the adjacent layers are also discussed.