论文标题
统一的floquet晶格，拓扑绝缘子及其非线性动力学的方法
Unified approach to Floquet lattices, topological insulators, and their nonlinear dynamics
论文作者
论文摘要
提出了一种分析与一类Floquet拓扑绝缘子相关的动力学和拓扑结构的统一方法。该方法应用于描述电磁波传播的系统，该系统通过二维晶格的大部分，该晶格朝向传播方向旋转。紧密结合近似用于得出减少的动力学系统。进一步的渐近近似值，在高频驾驶方案中有效，产生一个时间平均系统，该系统控制波浪的领先行为。从中，通过分析频谱临界点附近的本征函数的局部行为来对浆果连接，曲率和Chern数进行分析计算。例子包括蜂窝，Lieb和Kagome Lattices。在非线性制度中，衍生出慢慢变化的波信封的新颖方程。对于蜂窝晶格，数值模拟表明，对于相对较小的非线性效应，发生了惊人的螺旋模式。随着非线性的增加，局部结构的出现，并且在较高的非线性方面，波浪崩溃了。
A unified method to analyze the dynamics and topological structure associated with a class of Floquet topological insulators is presented. The method is applied to a system that describes the propagation of electromagnetic waves through the bulk of a two-dimensional lattice that is helically-driven in the direction of propagation. Tight-binding approximations are employed to derive reduced dynamical systems. Further asymptotic approximations, valid in the high-frequency driving regime, yield a time-averaged system which governs the leading order behavior of the wave. From this follows an analytic calculation of the Berry connection, curvature and Chern number by analyzing the local behavior of the eigenfunctions near the critical points of the spectrum. Examples include honeycomb, Lieb and kagome lattices. In the nonlinear regime novel equations governing slowly varying wave envelopes are derived. For the honeycomb lattice, numerical simulations show that for relatively small nonlinear effects a striking spiral patterns occurs; as nonlinearity increases localized structures emerge and for somewhat higher nonlinearity the waves collapse.
