Temperature evolution of the phonon dynamics in the Kitaev spin liquid

TL;DR

This paper investigates how fractionalized excitations in the Kitaev spin liquid influence phonon behavior at finite temperatures, revealing signatures in sound attenuation and Hall viscosity that could help identify such states in materials.

Contribution

It provides a detailed analysis of phonon dynamics affected by fractionalized excitations in the Kitaev model, combining analytical and numerical methods to explore temperature-dependent effects.

Findings

Attenuation coefficient's angular dependence is modified by Z2 fluxes.

Hall viscosity is suppressed with increasing Z2 flux density.

Thermal excitations influence phonon decay and symmetry-breaking effects.

Abstract

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.