Lo Po-Wei, Santangelo Christian D, Chen Bryan Gin-Ge, Jian Chao-Ming, Roychowdhury Krishanu, Lawler Michael J
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
Phys Rev Lett. 2021 Aug 13;127(7):076802. doi: 10.1103/PhysRevLett.127.076802.
Many advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topological invariant in a linear theory. In this Letter, we present a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of a topological index in differential geometry known as the Poincaré-Hopf index, which features the topological invariant of nonlinear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected nonlinear ZMs in the future.
拓扑力学领域已经取得了许多进展。然而，大多数工作都涉及线性理论中的拓扑不变量。在本信函中，我们提出了一种通用的方法来定义拓扑指标，该方法无需任何近似就能适应机械系统中的非线性效应。借助微分几何工具，预测了一个与微分几何中的拓扑指标（称为庞加莱 - 霍普夫指标）相关的整数值量，它表征了非线性零模（ZMs）的拓扑不变量。我们进一步确定了一种对无序具有鲁棒性的拓扑保护孤子类型。我们的方法构成了未来寻找新型拓扑保护非线性零模的一个新方向。
