For the Su–Schrieffer–Heeger (SSH) model on the two-dimensional square lattice, two third nearest neighbor hoppings which preserve chiral symmetry are introduced. Like the case of one dimension, the longer-range hopping can drive topological transitions and leads to the larger topological invariant (vectored Berry phase for the two dimensional SSH model). We obtain the phase boundaries and topological phase diagrams from the winding pattern of $\rho \left(k_l\right)$ of the Bloch Hamiltonian. The energy spectra and edge modes of the finite-sized model are also obtained. Effects of correlations on the extended two dimensional SSH model are investigated. The correlation shifts the phase boundaries and leads to topological transitions. Several special points in non-interacting phase diagrams are chosen to illustrate the different phase transitions and a correlations-driven topologically non-trivial phase from the trivial one is found. In this work, the slave-rotor mean field method is applied to the interacting model and we focus on the case of physical electrons, i.e. the Mott transition of charge degree of freedom is avoided in our investigations.

对于二维方格上的 Su-Schrieffer-Heeger (SSH) 模型，引入了两个保持手征对称性的第三最近邻跳跃。与一维的情况一样，更远距离的跳跃可以驱动拓扑转换并导致更大的拓扑不变量（二维 SSH 模型的矢量 Berry 相位）。我们从绕组模式中获得相边界和拓扑相图$\rho \left({克}_{升}\right)$布洛赫哈密顿量。还获得了有限尺寸模型的能谱和边缘模式。研究了相关性对扩展二维 SSH 模型的影响。相关性改变了相边界并导致拓扑转变。选择非相互作用相图中的几个特殊点来说明不同的相变，并从平凡的相中找到了相关性驱动的拓扑非平凡相。在这项工作中，从转子平均场方法应用于相互作用模型，我们关注物理电子的情况，即在我们的研究中避免了电荷自由度的莫特跃迁。