Topological Classical Systems with Generalized Chiral Symmetry

TL;DR

This paper explores how breaking generalized chiral symmetry in classical systems influences their topological properties, highlighting the role of on-site energy variations in determining topological phases and states.

Contribution

It introduces the impact of non-uniform on-site energy on topological phases in classical systems with broken generalized chiral symmetry, expanding the understanding of topological control.

Findings

On-site energy variations affect topological phases.

End lattice energy influences topological state existence.

Generalized chiral symmetry breaking alters topological properties.

Abstract

The bulk band topology of symmetry invariant adiabatic systems in the thermodynamic limit are considered to be determined by the hopping energy. In this work, we present that in closed classical systems, due to generalized chiral symmetry broken, the on-site energy cannot always be regarded as identical and can crucially impact the topological properties of the systems. Based on a finite one-dimensional chain, we demonstrate that the non-equivalent on-site energy of bulk lattices affects the topological phases of the bands, and the on-site energy of end lattices affects the existence of the topological states. Along these lines, the correspondence with generalized chiral symmetry in acoustic system is rigorously proposed. Our work provides a new degree of freedom for topological classical systems, and can be generalized to higher-dimensions and non-Hermitian conditions.