Phonon dynamics in the Kitaev spin liquid

Abstract

The search for fractionalization in quantum spin liquids largely relies on their decoupling with the environment. However, the spin-lattice interaction is inevitable in a real setting. While the Majorana fermion evades a strong decay due to the gradient form of spin-lattice coupling, the study of the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the signatures of fractionalization can be seen in the sound attenuation and the Hall viscosity. Despite the fact that both quantities can be related to the imaginary part of the phonon self-energy, their origins are quite different, and the time-reversal symmetry breaking is required for the Hall viscosity. First, we compute the sound attenuation due to a phonon scattering off of a pair of Majorana fermions and show that it is linear in temperature ($\sim T$). We argue that it has a particular angular dependence providing the information about the spin-lattice coupling and the low-energy Majorana fermion spectrum. The observable effects in the absence of time-reversal symmetry are then analyzed. We obtain the phonon Hall viscosity term from the microscopic Hamiltonian with time-reversal symmetry breaking term. Importantly, the Hall viscosity term mixes the longitudinal and transverse phonon modes and renormalize the spectrum in a unique way, which may be probed in spectroscopy measurement.

arXiv commentpublished version

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• Exceptional dynamics of interacting spin liquids
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• Phonon Dynamics in the Generalized Kitaev Spin Liquid
• Magnetic-field Induced Topological Transitions and Thermal Conductivity in a Generalized Kitaev Model
• Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids
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• Topological phase diagrams of in-plane field polarized Kitaev magnets
• Hydrostatic pressure effect on Co-based honeycomb magnet BaCo2(AsO4)2
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• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Sound attenuation in the hyperhoneycomb Kitaev spin liquid
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• Signatures of fractionalization in the optical phonons of hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Spin-phonon coupling and thermal Hall effect in the Kitaev model
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• Direct probe of magnetic field effects on phonons by ultrasound propagation in a quasi-two-dimensional honeycomb magnet Na${}_2$Co${}_2$TeO${}_6$