We report on the unusual behavior of the in-plane thermal conductivity κ and torque τ response in the Kitaev-Heisenberg material α-RuCl_{3}. κ shows a striking enhancement with linear growth beyond H=7  T, where magnetic order disappears, while τ for both of the in-plane symmetry directions shows an anomaly at the same field. The temperature and field dependence of κ are far more complex than conventional phonon and magnon contributions, and require us to invoke the presence of unconventional spin excitations whose properties are characteristic of a field-induced spin-liquid phase related to the enigmatic physics of the Kitaev model in an applied magnetic field.

Anomalous Thermal Conductivity and Magnetic Torque Response in the Honeycomb Magnet α−RuCl3

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ_{xx} due to phonons is much larger than the expected quantized thermal Hall conductance κ_{xy}^{q}=(πT/12)(k_{B}^{2}/ℏ) of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L≫ℓ, where ℓ is a thermalization length. We obtain ℓ∼T^{-5} for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κ_{xy}/κ_{xx}∼10^{-3}, in α-RuCl_{3}.

Quantization of the thermal Hall conductivity at small Hall angles

In recent years, it has been shown that the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the sound attenuation measurements allows for the characterization and identiﬁcation of the Kitaev quantum spin liquid on the hyperhoneycomb lattice, which is particularly interesting since the strong Kitaev interaction was observed in the the hyperhoneycomb magnet β -Li 2 IrO 3 . To this end we consider the low-temperature scattering between acoustic phonons and gapless Majorana fermions with nodal-line band structure. We ﬁnd that the sound attenuation has a characteristic angular dependence, which is explicitly shown for the high-symmetry planes at temperatures below the ﬂux energy gap.

/pdf/sound-attenuation-in-the-hyperhoneycomb-kitaev-spin-liquid-pu7bhs7i.pdf

Sound attenuation in the hyperhoneycomb Kitaev spin liquid

The quasi-two-dimensional $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ displays a unique two-step charge density wave (CDW) transition, from incommensurate (ICDW) to nearly commensurate (NCDW), and from NCDW to commensurate (CCDW), which is reflected in the stepwise resistivity behavior. In this work, we show that the hysteresis observed in the resistivity across the NCDW-to-CCDW transition is coupled to a local structure anomaly, evident from the pair density function analysis of neutron and x-ray diffraction data. We find that upon cycling the system from high to low temperatures (through the NCDW-CCDW transition) and collecting data on warming, local distortions in the in-star Ta and out-of-plane S atoms become evident, disrupting the trigonal symmetry of the star of David structures, without breaking the lattice periodicity, and preserving the underlying $\mathrm{P}\overline{3}$ symmetry. When the system is warmed up from the NCDW to the ICDW state, the local distortions are absent and the stars are symmetric, indicating that it is the thermal cycling through the NCDW-CCDW that locks in the distortions. Furthermore, we verify the temperature dependence of the two types of stacking along the $c$ axis: at low temperatures, the layer stacking exhibits a $13{\mathrm{c}}_{o}$ order that disappears upon warming through the NCDW transition, while across the NCDW and ICDW phases, the layer stacking is $3{\mathrm{c}}_{o}$. The $3{\mathrm{c}}_{o}$ order gradually disappears in the ICDW state. 

Local structure anomaly with the charge ordering transition of 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mi>T</mml:mi></mml:mrow><mml:mtext>−</mml:mtext><mml:msub><mml:mrow><mml:mi>TaS</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math>

We present a new mechanism for Raman scattering of phonons, which is based on the linear magnetoelastic coupling present in non-Kramers magnetic ions. This provides a direct coupling of Raman-active phonons to the magnet’s quasiparticles. We propose to use this mechanism to probe the emergent magnetic monopoles, electric charges, and photons of the emergent quantum electrodynamics (eQED) of the U(1) quantum spin liquid known as quantum spin ice. Detecting this eQED in candidate rare-earth pyrochlore materials, or indeed signatures of topological magnetic phases more generally, is a challenging task. We show that the Raman scattering cross-section of the phonons directly yields relevant information, with the broadening of the phonon linewidth, which we compute, exhibiting a characteristic frequency dependence reflecting the two-particle density of states of the emergent excitations. Remarkably, we find that the Raman linewidth is sensitive to the details of the symmetry fractionalisation and hence can reveal information about the projective implementation of symmetry in the quantum spin liquid, thereby providing a diagnostic for a π-flux phase. The Raman scattering of the phonons thus provides a useful experimental tool to probe the fractionalisation in quantum spin liquids that turns out closely to mirror pair production in quantum electrodynamics and the deep inelastic scattering of quantum chromodynamics. Indeed, the difference to the latter is conceptual more than technical: the partons (quarks) emerge from the hadrons at high energies due to asymptotic freedom, while those in eQED arise from fractionalisation of the spins at low energies.

Probing emergent QED in quantum spin ice via Raman scattering of phonons: Shallow inelastic scattering and pair production

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.

Fractional Excitation Induced Giant Phonon Anomalies in the Proximate Kitaev Quantum Spin Liquid $\alpha$-RuCl$_3$

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Fractional Excitation Induced Giant Phonon Anomalies in the Proximate Kitaev Quantum Spin Liquid $\alpha$-RuCl$_3$