Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$

Abstract

Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $\alpha$-RuCl${}_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $\alpha$-RuCl${}_3$. Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is either $\pm$1, as the Majorana band structure of the pure Kitaev spin liquid. This observation of a half-integer anomalous thermal Hall effect firmly establishes that the Kitaev interaction is primarily responsible and that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in $\alpha$-RuCl${}_3$.

14 pages, 4 figures

References in corpus (12)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Observation of the Magnon Hall Effect
• Models and Materials for Generalized Kitaev Magnetism
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Theory of the field-revealed Kitaev spin liquid
• Sign structure of thermal Hall conductivity for in-plane-field polarized Kitaev magnets
• Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions
• Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl${}_3$

Cited by in corpus (191)

• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• The planar thermal Hall conductivity in the Kitaev magnet α-RuCl3
• Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate $\alpha$-RuCl${}_3$
• Excitations in the ordered and paramagnetic states of honeycomb magnet Na2Co2TeO6
• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• A magnetic continuum observed by terahertz spectroscopy in a quantum spin liquid candidate BaCo${}_2$(AsO${}_4$)${}_2$
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• Giant magnetic in-plane anisotropy and competing instabilities in Na3Co2SbO6
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
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• Planar Thermal Hall Effects in Kitaev Spin Liquid Candidate Na2Co2TeO6
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
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