We study here a single band Hamiltonian model to describe the effect of next-nearest-neighbor (NNN) electron hopping on superconducting gap in Cuprates. The Hamiltonian consists of nearest-neighbor (NN) and next-nearest-neighbor (NNN) electron hopping integrals between the copper sides. By taking d-wave pairing symmetry into account, BCS type superconducting interaction is studied. By applying Zubarev’s Green function technique, the total Hamiltonian is solved. From the correlation function, the temperature-dependent superconducting gap (SC) equation is derived and is computed self-consistently by using technique [Formula: see text] grid points of the electron momentum. By varying SC coupling, chemical potential, J-T coupling parameter and second-nearest-neighbor electron hopping integral, the evolution of the order parameter is investigated.

中文翻译：

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次最近邻电子跳跃对铜酸盐超导体超导间隙的影响

我们在这里研究了一个单带哈密顿模型来描述次最近邻 (NNN) 电子跳跃对铜酸盐中超导间隙的影响。哈密​​顿量由铜边之间的最近邻 (NN) 和次最近邻 (NNN) 电子跳跃积分组成。考虑d波配对对称性，研究了BCS型超导相互作用。通过应用 Zubarev 的格林函数技术，求解了总哈密顿量。从相关函数，推导出温度相关的超导间隙 (SC) 方程，并通过使用技术 [公式：见文本] 电子动量的网格点自洽计算。通过改变SC耦合、化学势、JT耦合参数和第二近邻电子跳跃积分，研究了有序参数的演变。