Signatures of fractionalization in the optical phonons of hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$

Abstract

In this study, we propose that the signatures of spin fractionalization in quantum magnets can be identified through a detailed analysis of the temperature dependence of the asymmetric Fano lineshape of optical phonons overlapping with a continuum of spin excitations. We focus on the hyperhoneycomb magnet $\beta$-Li${}_2$IrO${}_3$, a promising candidate for being in proximity to a three-dimensional Kitaev quantum spin liquid. The Raman response in $\beta$-Li${}_2$IrO${}_3$ notably displays a distinctive asymmetric Fano lineshape in the 24 meV Raman-active optical phonon. This asymmetry arises from the interaction between the discrete phonon mode and the spin excitation continuum, which could be fractionalized if the material is indeed near a quantum spin-liquid phase. Our theoretical model considers the coupling of this optical phonon to Majorana fermions in the Kitaev model on the hyperhoneycomb lattice. Our findings reveal that the temperature-dependent Fano lineshape is consistent with the fractionalization of spins into Majorana fermions and $\mathbb{Z}{}_2$ fluxes.

17 pages, 9 figures

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