Klein-Gordon Representation of Acoustic Waves and Topological Origin of Surface Acoustic Modes

Abstract

Recently, it was shown that surface electromagnetic waves at interfaces between continuous homogeneous media (e.g., surface plasmon-polaritons at metal-dielectric interfaces) have a topological origin [K. Y. Bliokh et al., Nat. Commun. 10, 580 (2019)]. This is explained by the nontrivial topology of the non-Hermitian photon helicity operator in the Weyl-like representation of Maxwell equations. Here we analyze another type of classical waves: longitudinal acoustic waves corresponding to spinless phonons. We show that surface acoustic waves, which appear at interfaces between media with oppositesign densities, can be explained by similar topological features and the bulk-boundary correspondence. However, in contrast to photons, the topological properties of sound waves originate from the nonHermitian four-momentum operator in the Klein-Gordon representation of acoustic fields