# Topological band structure of surface acoustic waves on a periodically corrugated surface

## TL;DR

This paper theoretically demonstrates the emergence of topological edge modes in surface acoustic waves on a periodically corrugated surface, revealing Dirac cones, gap opening via symmetry breaking, and nonzero Chern numbers indicating topological protection.

## Contribution

It introduces a model for topological SAWs on a corrugated surface, analytically showing Dirac cones, gap opening, and nonzero Chern numbers, advancing understanding of topological phononic systems.

## Key findings

- Dirac cones appear at K and K' points due to corrugation.
- Breaking time-reversal symmetry opens a gap at Dirac points.
- The lowest band has a nonzero Chern number, indicating topological edge modes.

## Abstract

Surface acoustic waves (SAWs) are elastic waves localized on a surface of an elastic body. We theoretically study topological edge modes of SAWs for a corrugated surface. We introduce a corrugation forming a triangular lattice on the surface of an elastic body. We treat the corrugation as a perturbation, and construct eigenmodes on a corrugated surface by superposing those for the flat surface at wavevectors which are mutually different by reciprocal lattice vectors. We thereby show emergence of Dirac cones at the $K$ and $K'$ points analytically. Moreover, by breaking the time-reversal symmetry, we show that the Dirac cones open a gap, and that the Chern number for the lowest band has a nonzero value. It means existence of topological chiral edge modes of SAWs in the gap.