[Paper Review] Optical phonons coupled to a Kitaev spin liquid

A. Metavitsiadis, W. Natori+2 more|arXiv (Cornell University)|Mar 17, 2021

Advanced Condensed Matter Physics4 citations

TL;DR

This paper develops a microscopic theory of optical phonons coupled to a Kitaev spin liquid (KSL), showing that phonon line shapes acquire asymmetry due to Majorana fermion scattering and the Fano effect. It demonstrates that phonon lifetimes increase with temperature and that the coupling is insensitive to gauge fluxes and magnetic fields, providing a mechanism for the Fano-like line shapes observed in Raman scattering on α-RuCl₃.

ABSTRACT

Emergent excitation continua in frustrated magnets are a fingerprint of fractionalization, characteristic of quantum spin-liquid states. Recent evidence from Raman scattering for a coupling between such continua and lattice degrees of freedom in putative Kitaev magnets [1-6] may provide insight into the nature of the fractionalized quasiparticles. Here we study the renormalization of optical phonons coupled to the underlying $\mathbb{Z}_{2}$ quantum spin-liquid. We show that phonon line-shapes acquire an asymmetry, observable in light scattering, and originating from two distinct sources, namely the dispersion of the Majorana continuum and the Fano effect. Moreover, we find that the phonon life-times increase with increasing temperature due to thermal blocking of available phase space. Finally, in contrast to low-energy probes, optical phonon renormalization is rather insensitive to thermally excited gauge fluxes and barely susceptible to external magnetic fields.

Motivation & Objective

• To understand the origin of Fano-like line shapes in Raman scattering on Kitaev candidate materials like α-RuCl₃.
• To investigate how optical phonons are renormalized by fractionalized Majorana fermions in a Z₂ quantum spin liquid.
• To clarify the role of phonon-phonon mixing, temperature dependence, and external magnetic fields in the observed spectral features.
• To provide a microscopic framework linking phonon renormalization to the presence of fractionalized Majorana excitations in Kitaev systems.

Proposed method

• Formulates a total Hamiltonian combining free phonons (H_P), the Kitaev spin Hamiltonian (H_K), and a magnetoelastic spin-phonon coupling (H_KP).
• Computes the phonon self-energy Σ(ω) to determine the renormalized phonon spectral function, including contributions from the Majorana continuum and gauge fluxes.
• Uses a phenomenological approach to model the Raman response I(ω), incorporating Fano interference via effective coupling constants r_m and C_m.
• Applies the fluctuation-dissipation theorem to map the retarded propagator to the measurable Raman intensity I''(ω).
• Neglects phonon mixing for tractability, focusing on diagonal self-energy components D_{mm}(ω) and their impact on line shapes.
• Performs numerical calculations for two optical phonon modes (E_g1, E_g2) at finite temperature, analyzing frequency shifts and linewidths.

Experimental results

Research questions

• RQ1 What causes the asymmetric line shapes observed in Raman scattering on α-RuCl₃, and can they be attributed to coupling with fractionalized Majorana excitations?
• RQ2 How does temperature affect the lifetime and spectral width of optical phonons in a Kitaev spin liquid?
• RQ3 To what extent are phonon renormalizations influenced by thermally excited Z₂ gauge fluxes or external magnetic fields?
• RQ4 Can the Fano effect in Raman spectra be explained by coupling between optical phonons and the Majorana continuum?
• RQ5 How do the diagonal and off-diagonal components of the phonon self-energy contribute to the observed spectral features?

Key findings

• Phonon line shapes exhibit asymmetry due to two distinct mechanisms: the dispersion of the Majorana continuum and the Fano effect, with the latter causing a sharp drop-off on the high-frequency side.
• Phonon lifetimes increase with temperature, contrary to typical many-body systems, due to thermal blocking of phase space for decay processes.
• The coupling between optical phonons and Majorana fermions is weak, with off-diagonal elements D_{12} much smaller than diagonal ones, indicating negligible phonon mixing.
• The Raman response I''(ω) shows a broad magnetic continuum atop two asymmetric phonon peaks, closely matching experimental data from α-RuCl₃.
• The observed spectral features are largely insensitive to thermally excited gauge fluxes and external magnetic fields, distinguishing them from conventional spin-boson coupling effects.
• The qualitative agreement between theory and experiment supports the interpretation that the Fano line shapes originate from Majorana scattering, not just phonon-magnon coupling.