Superconductivity in Bilayer <i>t</i>–<i>t</i>? Hubbard Models

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