We investigate the higher-order topological insulators on the breathing kagome lattices with $p$-orbital freedom. The bulk topological phase diagram is obtained by calculating the $Z_3$ Berry phase of the $p$-band model. The existence of a different class of orbital corner states is demonstrated on the (zero-dimensional) finite-size triangular structure. We find that the transverse hopping of the $p$ orbital is essential for the corner states to appear on the finite-size structure. The orbital configurations of the corner states are also explored and rich orbital orders are identified. Moreover, we show that the orbital corner states can be realized in a realistic photonic system, which are in good agreement with the predictions of the tight-binding model and then offer a versatile platform for the orbital physics.

中文翻译：

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呼吸的kagome晶格上的轨道角状态

我们研究了呼吸Kagome格上的高阶拓扑绝缘子 $p$轨道自由。体拓扑相图是通过计算${ž}_3$ 浆果阶段 $p$带模型。在（零维）有限尺寸的三角形结构上，证明了存在另一类轨道角状态。我们发现，$p$轨道对于拐角状态出现在有限大小的结构上至关重要。还研究了转角状态的轨道配置，并确定了丰富的轨道顺序。此外，我们证明了可以在现实的光子系统中实现轨道角状态，这与紧束缚模型的预测非常吻合，然后为轨道物理学提供了一个通用平台。