Klein-Gordon representation of acoustic waves and topological origin of surface acoustic modes. (arXiv:1902.03614v2 [physics.class-ph] UPDATED)

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
opposite-sign 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 non-Hermitian
four-momentum operator in the Klein-Gordon representation of acoustic fields.

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