Approximately quantized thermal Hall effect of chiral liquids coupled to phonons

Abstract

The recent observation of a half-integer quantized thermal Hall effect in $\alpha$-RuCl${}_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity ${\kappa }_{x}y$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory. As an example we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $\Delta {\kappa }_{xy}/T\sim \text{sign(B)}{T}^2$, arises from a intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.

arXiv comment13 pages. Updated reference list

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• Hunting Majorana Fermions in Kitaev Magnets
• The 2021 Quantum Materials Roadmap
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• Finite field regime for a quantum spin liquid in $\alpha$-RuCl${}_3$
• 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
• Spin Wave Analysis of Low-Temperature Thermal Hall Effect in the Candidate Kitaev Spin Liquid $\alpha$-RuCl${}_3$
• 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
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• 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
• Giant Phonon Anomalies in the Proximate Kitaev Quantum Spin Liquid $\alpha$-RuCl${}_3$
• Phonon renormalization in the Kitaev quantum spin liquid
• Field-induced phase transitions of the Kitaev material $\alpha$-RuCl${}_3$ probed by thermal expansion and magnetostriction
• Giant thermal magnetoconductivity in CrCl${}_3$ and a general model for spin-phonon scattering
• Planar Thermal Hall Effects in Kitaev Spin Liquid Candidate Na2Co2TeO6
• Field-induced QCD${}_3$-Chern-Simons quantum criticalities in Kitaev materials
• 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
• Thermal Hall signatures of non-Kitaev spin liquids in honeycomb Kitaev materials
• Kitaev Quantum Spin Liquids
• High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb $\alpha$-Li${}_2$IrO${}_3$
• THz excitations in α-RuCl3: Majorana fermions, rigid-plane shear and compression modes
• Observation of a Chiral Wave Function in Twofold Degenerate Quadruple Weyl System BaPtGe
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Planar thermal Hall effect from phonons in a Kitaev candidate material
• Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids
• Phonon Hall viscosity from phonon-spinon interactions
• Temperature evolution of the phonon dynamics in the Kitaev spin liquid
• Heat transport in the anisotropic Kitaev spin liquid
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• Thermal Hall Effect in the Kitaev-Heisenberg System with Spin-Phonon Coupling
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• Flux mobility delocalization in the Kitaev spin ladder
• Non-Kitaev spin liquids in Kitaev materials
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Exceptional dynamics of interacting spin liquids
• Acoustic phonon dispersion of $\alpha$-RuCl${}_3$
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid
• Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets
• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Thermal Hall response: violation of gravitational analogues and Einstein relations
• 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
• Bulk thermal transport coefficients in a quantum Hall system and the fundamental difference between thermal and charge response
• Competition between Kondo and Kitaev Physics in Kitaev clusters coupled to a fermionic bath
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Torsion, energy magnetization and thermal Hall effect
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Phase diagram and thermal Hall conductivity of spin-liquid Kekulé-Kitaev model
• Chiral excitations and the intermediate-field spin-liquid regime in the Kitaev magnet $\alpha$-RuCl${}_3$
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