# Signatures of Topological Phonons in Superisostatic Lattices

## TL;DR

This paper investigates how topological surface phonons in idealized lattices manifest as finite-frequency modes in realistic superisostatic lattices, with implications for designing mechanical metamaterials.

## Contribution

It introduces a study of finite-frequency topological surface phonons in superisostatic lattices with added interactions, bridging ideal models and real-world materials.

## Key findings

- Finite-frequency surface phonons are present in superisostatic lattices.
- Signatures of topological modes persist despite added interactions.
- Results are relevant for designing mechanical metamaterials.

## Abstract

Soft topological surface phonons in idealized ball-and-spring lattices with coordination number $z=2d$ in $d$ dimensions become finite-frequency surface phonons in physically realizable superisostatic lattices with $z>2d$. We study these finite-frequency modes in model lattices with added next-nearest-neighbor springs or bending forces at nodes with an eye to signatures of the topological surface modes that are retained in the physical lattices. Our results apply to metamaterial lattices, prepared with modern printing techniques, that closely approach isostaticity.