论文标题
在$π$ -Flux Square晶格上的均衡性高阶高阶拓扑绝缘子
Out of equilibrium chiral higher order topological insulator on a $π$-flux square lattice
论文作者
论文摘要
批量拓扑的标志之一是存在强大的边界本地化状态。例如，常规的$ d $维拓扑系统托有$ d { - } 1 $尺寸表面模式，该模式受非空间对称性保护。最近，这个想法已扩展到具有边界模式的高阶拓扑阶段，这些阶段位于较低维度，例如在拐角处或系统的一维铰链中。在这项工作中，我们证明，当时间无关的模型不具有任何对称性受保护的拓扑状态时，可以在非平衡状态下设计高阶拓扑阶段。高阶拓扑受到新兴的手性对称性的保护，该对称是通过Floquet驱动而产生的。使用确切的数值方法和从Brillouin-Wigner扰动理论获得的有效的高频哈密顿量，我们在$π$ -Flux Square晶格上验证了新兴拓扑阶段。我们表明，我们模型中的局部角模式与保留扰动的手性对称性具有鲁棒性，并且可以归类为“外部”高阶拓扑阶段。最后，我们从相应的Sublattice对称的一维模型的绕组数中确定了二维拓扑不变。后一个模型属于拓扑问题十倍对称分类的AIII类。
One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial symmetries. Recently, this idea has been extended to higher order topological phases with boundary modes that are localized in lower dimensions such as in the corners or in one dimensional hinges of the system. In this work, we demonstrate that a higher order topological phase can be engineered in a nonequilibrium state when the time-independent model does not possess any symmetry protected topological states. The higher order topology is protected by an emerging chiral symmetry, which is generated through the Floquet driving. Using both the exact numerical method and an effective high-frequency Hamiltonian obtained from the Brillouin-Wigner perturbation theory, we verify the emerging topological phase on a $π$-flux square lattice. We show that the localized corner modes in our model are robust against a chiral symmetry preserving perturbation and can be classified as `extrinsic' higher order topological phase. Finally, we identify a two dimensional topological invariant from the winding number of the corresponding sublattice symmetric one dimensional model. The latter model belongs to class AIII of ten-fold symmetry classification of topological matter.
