Quantization of the thermal Hall conductivity at small Hall angles

Abstract

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 ${\kappa }_{xx}$ due to phonons is much larger than the expected quantized thermal Hall conductance ${\kappa }_{xy}^{\mathrm{q}}=\frac{\pi T}{12}\frac{k_B^2}{\hslash }$ 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 {\em 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 $L\gg \ell$, where $\ell$ is a thermalization length. We obtain $\ell \sim T^{-5}$ 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, ${\kappa }_{xy}/{\kappa }_{xx}\sim 10^{-3}$, in $\alpha$-RuCl${}_3$.

5+7 pages, 2 figures; v2: Improved the presentations for clarity, e.g., made some textual changes, showed temperature maps of the bulk and edges in Figure 1, added a summary of results in Table 1. Also added references. Published version

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Cited by in corpus (95)

• Quantum Spin Liquids
• A Field Guide to Spin Liquids
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Hunting Majorana Fermions in Kitaev Magnets
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• Phonons become chiral in the pseudogap phase of cuprates
• Sample dependence of the half-integer quantized thermal Hall effect in the Kitaev candidate $\alpha$-RuCl${}_3$
• Theory of the field-revealed Kitaev spin liquid
• Finite field regime for a quantum spin liquid in $\alpha$-RuCl${}_3$
• Approximately quantized thermal Hall effect of chiral liquids coupled to phonons
• Heisenberg-Kitaev physics in magnetic fields
• Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate $\alpha$-RuCl${}_3$
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Hunting for Majoranas
• Sign structure of thermal Hall conductivity for in-plane-field polarized Kitaev magnets
• Local Probes for Charge-Neutral Edge States in Two-Dimensional Quantum Magnets
• Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions
• Phonon dynamics in the Kitaev spin liquid
• Thermal Hall effects in quantum magnets
• Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl${}_3$
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Electrical Access to Ising Anyons in Kitaev Spin Liquids
• Electrical probes of the non-Abelian spin liquid in Kitaev materials
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
• Magnetoelastic coupling and effects of uniaxial strain in $\alpha$-RuCl${}_3$ from first principles
• Large contribution of Fermi arcs to the conductivity of topological metals
• Phonon renormalization in the Kitaev quantum spin liquid
• Giant Phonon Anomalies in the Proximate Kitaev Quantum Spin Liquid $\alpha$-RuCl${}_3$
• Giant thermal magnetoconductivity in CrCl${}_3$ and a general model for spin-phonon scattering
• Planar Thermal Hall Effects in Kitaev Spin Liquid Candidate Na2Co2TeO6
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Field-induced QCD${}_3$-Chern-Simons quantum criticalities in Kitaev materials
• Significant thermal Hall effect in the 3$d$ cobalt Kitaev system $N{a}_{2}C{o}_{2}Te{O}_6$
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet $\alpha$-RuCl${}_3$
• Current- and field-induced topology in twisted nodal superconductors
• Unfolding the complexity of quasi-particle physics in disordered materials
• Thermal Transport for Probing Quantum Materials
• Thermal Hall signatures of non-Kitaev spin liquids in honeycomb Kitaev materials
• Kitaev Quantum Spin Liquids
• THz excitations in α-RuCl3: Majorana fermions, rigid-plane shear and compression modes
• Planar thermal Hall effect from phonons in a Kitaev candidate material
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Observation of a Chiral Wave Function in Twofold Degenerate Quadruple Weyl System BaPtGe
• Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids
• Phonon Hall viscosity from phonon-spinon interactions
• Heat transport in the anisotropic Kitaev spin liquid
• Temperature evolution of the phonon dynamics in the Kitaev spin liquid
• Chiral spin-order in some purported Kitaev spin-liquid compounds
• Thermal Hall Effect in the Kitaev-Heisenberg System with Spin-Phonon Coupling
• Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces
• Interfacial Spin Seebeck effect in noncollinear magnetic systems
• Thermal anyon interferometry in phonon-coupled Kitaev spin liquids
• Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state
• Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model
• Footprints of the Kitaev spin liquid in the Fano lineshapes of the Raman active optical phonons
• Topological thermal Hall effect for topological excitations in spin liquid: Emergent Lorentz force on the spinons
• Thermal interferometry of anyons in spin liquids
• Flux mobility delocalization in the Kitaev spin ladder
• Hydrodynamics of three-dimensional skyrmions in frustrated magnets
• Non-Kitaev spin liquids in Kitaev materials
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Stacking disorder in $\alpha$-RuCl${}_3$ via x-ray three-dimensional difference pair distribution function analysis
• Exceptional dynamics of interacting spin liquids
• Magnetic vortex liquid and anomalous thermal Hall conductivity in frustrated magnets with bond-dependent interactions
• Topological Weyl magnons and thermal Hall effect in layered honeycomb ferromagnets
• Acoustic phonon dispersion of $\alpha$-RuCl${}_3$
• Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Thermal Hall response: violation of gravitational analogues and Einstein relations
• Magnetothermal transport in ultraclean single crystals of Kitaev magnet $\alpha$-RuCl${}_3$
• Measuring Topological Order
• Topological phase diagrams of in-plane field polarized Kitaev magnets
• Observation of Anomalous Thermal Hall Effect in a Kagome Superconductor
• Extended Quantum Spin Liquid with Spinon-like Excitations in an Anisotropic Kitaev-Gamma Model
• Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids
• Competition between Kondo and Kitaev Physics in Kitaev clusters coupled to a fermionic bath
• Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response
• Gauge Field Dynamics in Multilayer Kitaev Spin Liquids
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Torsion, energy magnetization and thermal Hall effect
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Chiral excitations and the intermediate-field spin-liquid regime in the Kitaev magnet $\alpha$-RuCl${}_3$
• Phase diagram and thermal Hall conductivity of spin-liquid Kekulé-Kitaev model
• Quantized thermal Hall conductance from edge current calculations in lattice models
• Magnetic field induced partially polarized chiral spin liquid in a transition metal dichalcogenide moiré system
• Quantum Spin Liquid phases in Kitaev Materials
• Extrinsic contribution to bosonic thermal Hall transport
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality
• The Role of the Third Dimension in Searching Majorana Fermions in $\alpha$-RuCl${}_3$ via Phonons
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Time-domain anyon interferometry in Kitaev honeycomb spin liquids and beyond