Surface phonon Hall viscosity in magnetic topological insulators

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, leading to a variety of topological response phenomena in magnetic topological insulators. In this work, we propose an acoustic analog to this phenomenon - the surface phonon Hall viscosity - that occurs at the surface or interface of magnetic topological insulator materials such as MnBi₂Te₄ and Eu-based Zintl compounds. This surface phonon Hall viscosity originates from the Nieh-Yan term in the strain response of topological insulators, where strain acts as the effective tetrad field for the bulk low-energy massive Dirac fermions. Consequently, localized surface phonon modes with nonzero orbital angular momentum emerge and give rise to a variety of physical phenomena, including effective phonon magnetic moments, acoustic Faraday and Cotton-Mouton rotation, and thermal Hall effect at the surface of magnetic topological insulators. Additionally, we demonstrate that surface magnon modes couple to these surface phonon modes, yielding hybridized magnon-phonon collective excitations.