Fundamentals of 1D and 2D lattice-based mechanical topological insulators (Conference Presentation)

Abstract

Spring-mass lattices constitute an accessible model for the understanding of various physical phenomena. Here, they are used to probe fundamental aspects of mechanical topological insulators. First, in gapped one-dimensional 2-periodic lattices, a simple interpretation of Zack’s phase and of the associated integer winding number is provided based on the stiffness coupling two consecutive masses. Nearest neighbor and non-nearest neighbor interactions are explored so as to generate more diverse winding numbers. Lattices with different winding numbers are shown to be topologically distinct. In that case, the difference in winding numbers is interpreted as a count of edge modes localized at the interface between the two topologically distinct lattices. The existence of these edge modes is verified through numerical modal analysis and through homogenization-type asymptotic analysis. The study is extended to two-dimensional systems. Although a visualization of the winding number, also known as a Chern number in this context, is harder, various aspects remain unchanged. Most importantly, an interface separating two topologically distinct gapped lattices will carry a number of edge modes. Last, robustness and immunity to back scattering of localized interface modes against defects is assessed for different systems.