Dissipationless phonon Hall viscosity

Maissam Barkeshli, Suk Bum Chung, Xiao Liang Qi

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42 Scopus citations


We study the acoustic phonon response of crystals hosting a gapped time-reversal symmetry-breaking electronic state. The phonon effective action can in general acquire a dissipationless "Hall' viscosity, which is determined by the adiabatic Berry curvature of the electron wave function. This Hall viscosity endows the system with a characteristic frequency ω v; for acoustic phonons of frequency ω, it shifts the phonon spectrum by an amount of order (ω /ω v )2 and it mixes the longitudinal and transverse acoustic phonons with a relative amplitude ratio of ω/ω v and with a phase shift of ±π/2, to lowest order in ω/ω v. We study several examples, including the integer quantum Hall states, the quantum anomalous Hall state in Hg 1-yMn yTe quantum wells, and a mean-field model for p x+ip y superconductors. We discuss situations in which the acoustic phonon response is directly related to the gravitational response, for which striking predictions have been made. When the electron-phonon system is viewed as a whole, this provides an example where measurements of Goldstone modes may serve as a probe of adiabatic curvature of the wave function of the gapped sector of a system.

Original languageEnglish
Article number245107
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number24
StatePublished - 7 Jun 2012


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