论文标题
方形根部高阶拓扑绝缘子在装饰的蜂窝状晶格上
Square-root higher-order topological insulator on a decorated honeycomb lattice
论文作者
论文摘要
方形拓扑绝缘子是最近提供的有趣的拓扑绝缘子，在该拓扑绝缘子中，Bloch波函数的拓扑性质性质是从Hamiltonian正方形继承的。在本文中，我们提出，高阶拓扑绝缘子也可以具有其平方根的后代，我们将其称为正方形的高阶拓扑绝缘子。在那里，距离内角状态的出现是从托有高阶拓扑的平方哈密顿量继承的。作为此类系统的一个例子，我们研究了装饰的蜂窝晶格上的紧密结合模型，其平方汉密尔顿包括呼吸的kagome-rattice模型，这是高阶拓扑绝缘子的众所周知的例子。我们表明，间隙角状态出现在有限的能量上，这与非平凡的散装极化相吻合。我们进一步表明，间隙拐角状态的存在导致特征性的单粒子动力学，即设置要定位在角落的初始状态，即使很长一段时间后，粒子仍在角落。在光子晶体中可以在实验上检测到这种特征动力学。
Square-root topological insulators are recently-proposed intriguing topological insulators, where the topologically nontrivial nature of Bloch wave functions is inherited from the square of the Hamiltonian. In this paper, we propose that higher-order topological insulators can also have their square-root descendants, which we term square-root higher-order topological insulators. There, emergence of in-gap corner states is inherited from the squared Hamiltonian which hosts higher-order topology. As an example of such systems, we investigate the tight-binding model on a decorated honeycomb lattice, whose squared Hamiltonian includes a breathing kagome-lattice model, a well-known example of higher-order topological insulators. We show that the in-gap corner states appear at finite energies, which coincides with the non-trivial bulk polarization. We further show that the existence of in-gap corner states results in characteristic single-particle dynamics, namely, setting the initial state to be localized at the corner, the particle stays at the corner even after a long time. Such characteristic dynamics may experimentally be detectable in photonic crystals.
