广义三方Haldane模型的拓扑相
Topological phases of a generalised tripartite Haldane model
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中文总结 AI 辅助
该研究提出广义三方Haldane模型，计算其陈数拓扑相图，发现其陈数绝对值可达7，部分内容可解析，还分析了远离高对称点的能级交叉演化。
中文摘要 AI 辅助
我们提出了一个具有复最近邻 hopping 参数的广义三方 Haldane 模型。该模型的原胞包含三个六角原胞，穿过原胞的总磁通量为零，因此具有环电流模型的结构。在最近邻与次近邻 hopping 参数幅度比固定的情况下，我们计算了陈数随这两个 hopping 参数相位变化的拓扑相图。结果表明，与 Haldane 模型不同，该模型的拓扑相图非常复杂，但部分内容仍可通过解析方法处理。此外，其拓扑相的陈数绝对值可达 7。布里渊区高对称点处能带交叉的显式表达式为分析提供了支撑，这些交叉表现为相图中的线性相界线，可解释拓扑相图的诸多特征。最后，我们分析了几个远离高对称点的能级交叉性质的代表性例子，以及它们随模型参数的演化情况。
英文摘要
We present a generalised tripartite Haldane model with a complex nearest neighbour hopping parameter. The total magnetic flux through the primitive unit cell, which consists of three hexagonal unit cells is zero, and thus the model has the structure of a loop-current model. We calculate topological phase diagrams of the Chern numbers as a function of the phases of the nearest and next-nearest neighbour hopping parameters for a fixed ratio of the magnitude of the hopping parameters. We show that, unlike the Haldane model, the topological phase diagram of this model is very complex, but some aspects can still be dealt with analytically. Furthermore, the Chern numbers of the topological phases are as large as $7$ in absolute value. The analysis is supported by explicit expressions for energy bands crossing at high symmetry points in the Brillouin zone, which show as linear phase boundaries in the phase diagram. We show that such lines explain many features in the topological phase diagrams. Finally, we analyse a few representative examples of the nature of level crossings away from high symmetry and their evolution with model parameters.
