Perfect deporalization of the Loudon-Fleury inelastic visible-light scattering in the Kitaev honeycomb model is well known. Though it happens in Heisenberg Kagome and triangular antiferromagnets as well, yet we prove it to be of geometric origin rather than peculiar to quantum spin liquids. A Kitaev spin liquid in the square planar geometry indeed exhibits polarized Raman spectra containing defferent symmetry species, each brought by symmetry-compatible spinon geminate excitations, i.e. arising from symmetry-compatible direct-product representations made of double-valued irreducible representations of mediating-spinon-belonging gauged
k-point symmetry groups. We combine a standard point-symmetry-group analysis of the Raman vertex in the real space and an elaborate projective-symmetry-group analysis of Raman-scattering-mediating Majorana spinons in the reciprocal space to identify emergent spinons singly.
Abstract We demonstrate a Kitaev spin liquid in a polyhedral cluster and propose detecting its fractional excitations—Majorana spinons—by magnetic Raman scattering. While little polarization dependence of the Raman spectra at sufficiently low temperatures is usual with quantum spin liquids, the present observations are primarily of geometric origin. The Raman scattering intensity peaks melt with increasing temperature, to be more precise, with increasing number of background gauge-flux excitations.
The excitation spectrum of Kitaev quantum spin liquids consists of itinerant Majorana fermions, which can be gapless or gapped, and vortices of a
Z2 gauge field, known as visons, which are \new{gapped within a stable
Z2 spin liquid phase}. In this work, we investigate visons in Kitaev-type models where the Majorana fermions form a Fermi surface. In this case, the creation of a vison pair is analogous to introducing a local impurity potential in a metal. Since the gapless modes lead to strong finite-size effects, we compare the numerical calculation of the \new{two-vison gap} on finite lattices with the result from an analytical approach based on Green's function techniques. We find that the \new{two-vison gap} decreases as the size of the Fermi surface increases, signalling an instability of the quantum spin liquid ground state. We also show that larger Fermi surfaces tend to suppress the change in local spin correlations due to the Majorana-vison scattering potential.
We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide observable signatures of fractionalized excitations characteristic of the underlying spin-liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonian based on the
D3d symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low-temperature crossover shows pronounced magnetic-field dependence. We thus identify the observable effect of the Majorana fermions and the
Z2 gauge fluxes encoded in the Fano lineshape. Our results are consistent with the phonon Raman scattering experiments in the candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$.
Projective symmetry groups are applied to Raman observations of the Kitaev quantum spin liquids in spherical lattice geometries realized by Platonic and Archimedean polyhedra. Parton single excitations in Kitaev spin polyhedra are characterized by double-valued irreducible representations of their belonging projective symmetry groups, whereas parton geminate excitations relevant to Raman scattering are decomposed into single-valued irreducible representations of the corresponding point symmetry groups. We combine a standard point symmetry group analysis of the Loudon-Fleury vertices and an elaborate projective symmetry group analysis of itinerant spinons against the ground gauge fields to reveal hidden selection rules for Raman scattering in
Z2 spin liquids.
Motivated by growing evidence for the significance of the third-nearest-neighbor Heisenberg (
J3) interaction in candidate Kitaev materials, we investigate the dynamical properties of the Kitaev spin liquid (KSL) under a
J3 perturbation, focusing on its spin dynamical structure factor (DSF) and Raman scattering. Within a self-consistent parton mean-field plus random-phase approximation framework, we find that
J3 induces coherent, paramagnon-like collective modes that coexist with a high-energy Majorana continuum in the spin DSF. The softening of these modes with increasing
∣J3∣ signals a quantum phase transition to magnetic order. Remarkably, magnetic ordering sets in at a common critical
J3 for both ferromagnetic (
K<0) and antiferromagnetic (
K>0) Kitaev models, with the resulting ordered states forming exact dual pairs under a four-sublattice duality transformation that maps
(K,J3)→(−K,J3). An external magnetic field further softens the preexisting paramagnon modes, thereby enhancing magnetic order. Perturbative Raman calculations show that while the Kitaev-like Raman vertex probes only itinerant matter Majorana fermions, the response from the
J3-like vertex features both matter Majoranas and visons. Four-vison excitations produce a sharp peak accompanied by a two-fermion continuum, whereas two-vison excitations yield a continuum closely resembling the single-matter-fermion density of states. These results provide a unified perspective on the dynamical signatures of
J3-perturbed KSL and are helpful for interpreting experimental spectra in candidate Kitaev materials with sizable
J3 interactions.