We study the sodium-iridates model on the honeycomb lattice with both BCS pairing potential and Hubbard interaction term. It is shown that this model can be exactly solved with appropriate choices of amplitude of pairing gaps, where the interacting terms are transformed to external field terms. The band structures of these exact solutions on both torus and cylinder geometry are discussed in great details. It is found that the ground state assumes an anti-ferromagnetic configuration, which breaks the time reversal symmetry spontaneously and renders the superconductor topologically trivial. On the other hand, the nontrivial topology is preserved with ferromagnetic configuration and can be characterized by the isospin Chern number.

中文翻译：

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Sodium-Iridate-BCS-Hubbard 模型沿对称线的精确解：铁磁序中的非平凡拓扑

我们研究了具有 BCS 配对势和 Hubbard 相互作用项的蜂窝晶格上的钠-铱酸盐模型。结果表明，该模型可以用适当的配对间隙的幅度选择，其中交互术语转换为外部场术语。详细讨论了圆环和圆柱几何上的这些精确解的能带结构。发现基态呈现反铁磁构型，它自发地打破时间反演对称性并使超导体在拓扑上微不足道。另一方面，非平凡拓扑保留了铁磁配置，并且可以用等旋陈数来表征。