Surface phonon Hall viscosity induced phonon chirality and nonreciprocity in magnetic topological insulator films

The surface half-quantum Hall effect, a hallmark consequence of axion electrodynamics, can be induced by gapping out the surface states of topological insulators through surface magnetization, and has led to a variety of topological response phenomena observed in experiments. In this work, we investigate phonon dynamics originating from an acoustic analog—the surface phonon Hall viscosity—that can also occur at the surface of magnetic topological insulators. This surface phonon Hall viscosity stems from the Nieh-Yan action in the strain response of topological insulators, where strain acts as the effective vierbein field for the bulk low-energy massive Dirac fermions. Crucially, this viscosity term entangles phonon dynamics with surface magnetization. In magnetic topological insulator films, we find that this interaction causes acoustic phonons to become chiral when the magnetization at the top and bottom surfaces is parallel, and nonreciprocal when it is anti-parallel. We further discuss potential experimental signatures of phonon dynamics induced by surface phonon Hall viscosity, specifically the phonon thermal Hall effect and magnon-polarons.