Topology in Nonlinear Mechanical Systems

Po-Wei Lo, Christian D. Santangelo, Bryan Gin-ge Chen, Chao-Ming Jian, Krishanu Roychowdhury, and Michael J. Lawler

Phys. Rev. Lett. 127, 076802 – Published 13 August 2021

Abstract

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.

Received 26 April 2021
Accepted 13 July 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.076802

Physics Subject Headings (PhySH)

Geometric & topological phases Mechanical & acoustical properties Mechanical deformation Origami & Kirigami Self-assembly Topological phases of matter

Polymers & Soft MatterNonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Po-Wei Lo ¹, Christian D. Santangelo², Bryan Gin-ge Chen³, Chao-Ming Jian¹, Krishanu Roychowdhury⁴, and Michael J. Lawler ^1,5

¹Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
²Department of Physics, Syracuse University, Syracuse, New York 13244, USA
³Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
⁴Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
⁵Department of Physics, Applied Physics and Astronomy, Binghamton University, Binghamton, New York 13902, USA