论文标题
双层中的超导率$ t $ - $ t'$哈伯德模型
Superconductivity in bilayer $t$-$t'$ Hubbard models
论文作者
论文摘要
晶体结构与超导临界温度之间的关系引起了极大的关注，这是设计更高$ t _ {\ rm c} $超导体的线索。特别是，Cuo $ _2 $的数字$ n $之间的关系是库酸酯超导体的单元和最佳超导过渡温度$ t _ {\ rm c}^{\ rm opt} $之间的关系。正如在分层丘比特中观察到的，$ t _ {\ rm c}^{\ rm opt} $在增加$ n $时增加，最高$ n = 3 $，然后，对于较大的$ n $，则减少。但是，$ n $依赖性背后的机制是$ t _ {\ rm c}^{\ rm opt} $，尽管有许多关于$ n $依赖性的研究，但仍然难以捉摸。在本文中，我们研究了双层$ t $ - $ t'ubbard型号，以阐明相邻的cuo $ _2 $层对超导性稳定性的影响，并使用多种可变量的变量蒙特卡洛方法。我们计算长距离和零温度的超导相关性，以及从动量分布估算的超导间隙函数的幅度，因为可观察到与$ t _ {\ rm c}^{\ rm opt} $相关。发现与单层$ t $ - $ t'$ Hubbard模型相比，平面内超导相关性并没有增强。与单层汉密尔顿（Hamiltonian）相比，双层汉密尔顿（Hamiltonian）双层汉密尔顿（Hamiltonian）的超导相关性显着很小，这归因于van Hove的奇异性。此外，我们发现，在最佳掺杂的单层和双层$ t $ -t $ t'$ hubbard模型中，超导间隙函数的幅度也相似。因此，我们得出的结论是，相邻的哈伯德层与BiLayer Cuprates中的$ t _ {\ rm c}^{\ rm opt} $的增强无关。还讨论了增强的$ t _ {\ rm c}^{\ rm opt} $的可能起源。
The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-$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.
