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Register a new userTemperature evolution of the phonon dynamics in the Kitaev spin liquid
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Here we present a study of the phonon dynamics in the honeycomb Kitaev spin model at finite temperatures. We show that the fractionalized spin excitations of the Kitaev spin liquid, the itinerant Majorana fermions and static $Z_2$ fluxes, have distinct effects on the phonon dynamics, which makes the phonon dynamics a promising tool for exploring the Kitaev spin liquid candidate materials. In particular, we will focus on the signature of the fractionalized excitations in the thermodynamic behaviour of the sound attenuation and the phonon Hall viscosity: The former describes the phonon decay into the fractionalized excitations, and the later is the leading order time reversal symmetry breaking effect on the acoustic phonon. We find that the angular dependence of the attenuation coefficient and its magnitude are modified by the thermal excitation of the $Z_2$ fluxes. The strength of this effect strongly depends on the relative magnitude of the sound velocity and the Fermi velocity characterizing the low-energy Majorana fermions. We also show that the Hall viscosity is strongly suppressed by the increase of the density of the $Z_2$ fluxes at finite temperatures. All these observations reflect the effects of the emergent disorder on the Majorana fermions introduced by the $Z_2$ fluxes. Our analysis is based on the complementary analytical calculations in the low-temperature zero-flux sector, and numerical calculations in the inhomogeneous flux sectors at intermediate and high temperatures with stratified Monte Carlo (strMC) method.
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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.
We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the $Gamma$, $K$ and $K$ points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $alpha$-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. This fractional excitation induced phonon anomalies uncover the key ingredient of the quantum thermal Hall effect in $alpha$-RuCl3 and demonstrates a proof-of-principle method to detect fractional excitations in topological quantum materials.
We study the spin-$S$ Kitaev model in the classical ($S to infty$) limit using Monte Carlo simulations combined with semi-classical spin dynamics. We discuss differences and similarities in the dynamical structure factors of the spin-$1/2$ and the classical Kitaev liquids. Interestingly, the low-temperature and low-energy spectrum of the classical model exhibits a finite energy peak, which is the precursor of the one produced by the Majorana modes of the $S=1/2$ model. The classical peak is spectrally narrowed compared to the quantum result and can be explained by magnon excitations within fluctuating one-dimensional manifolds (loops). Hence the difference from the classical limit to the quantum limit can be understood by the fractionalization of magnons propagating in one-dimensional manifolds. Moreover, we show that the momentum space distribution of the low-energy spectral weight of the $S=1/2$ model follows the momentum space distribution of zero modes of the classical model.
Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin liquid phase in the Kitaev material $alpha$-$mathrm{RuCl}_{3}$. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquids hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to `perfectly convert electrons from the former into emergent fermions in the latter---thereby enabling variations of transport probes invented for topological superconductors and fractional quantum Hall states. Along the way we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway towards topological quantum computation with Kitaev materials.
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