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.
Highlights
Quantum spin liquids (QSLs), a fascinating class of frustrated magnets, have been a focus of condensedmatter research since the initial proposal [1]
We study the observable consequences of the spin-lattice coupling through the phonon dynamics
We study the modifications of the phonon dynamics in the absence of time-reversal symmetry due to applying a magnetic field h
Summary
Quantum spin liquids (QSLs), a fascinating class of frustrated magnets, have been a focus of condensedmatter research since the initial proposal [1]. PHONON DYNAMICS IN THE KITAEV SPIN LIQUID αs is not changed qualitatively in a small magnetic field when (h/JK ) q a, where a is the lattice constant, the Majorana-fermion–phonon coupling introduces another interesting effect to the phonon system, i.e., a Berry phase term that mixes the transverse and longitudinal phonon modes. It is encoded in the phonon long-wavelength effective action as the Hall viscosity term, which is the leading-order term breaking the time-reversal symmetry [48,49]. IV we will use the Majorana-fermion representation of the spins to express the spin-phonon coupling Hc in terms of the free Majorana fermion cr and lattice displacement field uq,ν
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