Edge States with Hidden Topology in Spinner Lattices

TL;DR

This paper introduces a spring-mass model with hidden symmetries that reveal topological edge states, demonstrating their distinct profiles, robustness, and potential for advanced material design in various physical systems.

Contribution

It uncovers hidden symmetries in a spring-mass model that lead to novel topological edge states with distinct profiles at opposite edges, extending understanding beyond canonical models.

Findings

Edge states originate from hidden symmetries in deformation coordinates.

Edge states are experimentally observed with distinct profiles at opposite edges.

Edge states are robust against disorder respecting hidden symmetry.

Abstract

Symmetries -- whether explicit, latent, or hidden -- are fundamental to understanding topological materials. This work introduces a prototypical spring-mass model that extends beyond established canonical models, revealing topological edge states with distinct profiles at opposite edges. These edge states originate from hidden symmetries that become apparent only in deformation coordinates, as opposed to the conventional displacement coordinates used for bulk-boundary correspondence. Our model, realized through the intricate connectivity of a spinner chain, demonstrates experimentally distinct edge states at opposite ends. By extending this framework to two dimensions, we explore the conditions required for such edge waves and their hidden symmetry in deformation coordinates. We also show that these edge states are robust against disorders that respect the hidden symmetry. This research paves the way for advanced material designs with tailored boundary conditions and edge state profiles, offering potential applications in fields such as photonics, acoustics, and mechanical metamaterials.