AI 中文总结
该研究在实现量子自旋霍尔效应的二维机械拓扑绝缘体中，构造含相反自旋陈数的体晶格界面，利用耦合非线性薛定谔方程得到多种矢量边缘孤子，其具拓扑保护性，可用于碰撞计算，提升机械器件信息处理潜力。
AI 中文摘要
我们报道了二维机械拓扑绝缘体中的非线性边缘波。体晶格由具有 onsite 三次非线性的摆组成，摆通过线性弹簧连接，实现量子自旋霍尔效应。我们表明，两个具有相等群速度（EGV）的边缘模式之间的非线性相互作用由一维双分量耦合非线性薛定谔（CNLS）方程描述。在分隔两个具有相反自旋陈数的体晶格的界面上，我们构造线性弹簧使得色散关系呈现具有有利 CNLS 系数的 EGV 点。因此，我们实现了沿界面传播的非线性边缘波，包括聚焦 CNLS 系数对应的亮-亮（BB）边缘孤子，以及散焦 CNLS 系数对应的暗-暗边缘孤子、边缘畴壁和暗-亮边缘孤子。就格点振幅而言，这些解类似亮和暗呼吸子。当两个载波频率均处于带隙内时，这些解应具有拓扑保护性，我们通过让 BB 边缘孤子穿过界面上的紧凑缺陷明确证明了这一点。我们还展示了 BB 边缘孤子碰撞中的能量转移，其具有基于碰撞的计算的潜在应用。总体而言，矢量边缘孤子为孤子碰撞提供了大的参数空间，这赋予机械器件在信息处理和其他功能方面更大的潜力。
英文摘要
We report nonlinear edge waves in a 2D mechanical topological insulator. A bulk lattice consists of pendulums with on-site cubic nonlinearity connected by linear springs realizing quantum spin Hall effect. We show that the nonlinear interaction between two edge modes with equal group velocities (EGV) is described by a 1D two-component coupled nonlinear Schrödinger (CNLS) equation. On the interface separating two bulk lattices with opposite spin Chern numbers, we construct linear springs such that the dispersion relation exhibits EGV points with favorable CNLS coefficients. Thus, we realize nonlinear edge waves propagating along the interface, including bright-bright (BB) edge solitons for focusing CNLS coefficients, and dark-dark edge solitons, edge domain walls, and dark-bright edge solitons for defocusing CNLS coefficients. In terms of the site amplitudes, these solutions resemble bright and dark breathers. These solutions should be topologically protected when both carrier frequencies lie within a band gap, which we explicitly show by passing BB edge solitons through compact defects on the interface. We also show energy transfer in BB edge soliton collisions with potential application to collision-based computing. Generally, vector edge solitons exhibit a large parameter space for soliton collisions, which endows mechanical devices with greater potential for information processing and other functionalities.
Comments18 pages, 10 figures
