Higher-order topological phases are characterized by protected states localized at the corners or hinges of the system. By applying time-periodic quenches to a two-dimensional lattice with balanced gain and loss, we obtain a rich variety of non-Hermitian Floquet second-order topological insulating phases. Each of the phases is characterized by a pair of integer topological invariants, which predict the numbers of non-Hermitian Floquet corner modes at zero and $\pi$ quasienergies. We establish the topological phase diagram of the model and find a series of non-Hermiticity-induced transitions between different Floquet second-order topological phases. We further generalize the mean chiral displacement to two-dimensional non-Hermitian systems and use it to extract the topological invariants of our model dynamically. This paper thus extends the study of higher-order topological matter to more generic nonequilibrium settings, in which the interplay between Floquet engineering and non-Hermiticity yields fascinating phases.

中文翻译：

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周期淬火晶格中的非Hermitian Floquet二阶拓扑绝缘子

高阶拓扑阶段的特征是受保护状态位于系统的角或铰链处。通过将时间周期淬火应用于具有平衡增益和损耗的二维晶格，我们获得了种类繁多的非Hermitian Floquet二阶拓扑绝缘相。每个阶段都由一对整数拓扑不变量来表征，它们预测零和非零时的非Hermitian Floquet角模数。$\pi$准能量。我们建立了该模型的拓扑相图，并发现了在不同的Floquet二阶拓扑相之间的一系列非费米性诱导的转变。我们进一步将平均手性位移推广到二维非Hermitian系统，并使用它来动态提取模型的拓扑不变量。因此，本文将高阶拓扑问题的研究扩展到了更通用的非平衡设置，其中Floquet工程与非Hermiticity之间的相互作用产生了令人着迷的阶段。