Phonon Thermal Hall Conductivity from Scattering with Collective Fluctuations

Abstract

Because electrons and ions form a coupled system, it is a priori clear that the dynamics of the lattice should reflect symmetry breaking within the electronic degrees of freedom. This has been recently clearly evidenced for the case of time-reversal and mirror symmetry breakings by observations of a large phononic thermal Hall effect in many strongly correlated electronic materials. The mechanism by which time-reversal breaking and chirality is communicated to the lattice is, however, far from evident. In this paper we discuss how this occurs via many-body scattering of phonons by collective modes: a consequence of non-Gaussian correlations of the latter modes. We derive fundamental new results for such skew (i.e. chiral) scattering and the consequent thermal Hall conductivity. From this we also obtain general formulae for these quantities for ordered antiferromagnets. From the latter we obtain the scaling behavior of the phonon thermal Hall effect in clean antiferromagnets. The calculations show several different regimes and give quantitative estimates of similar order to that seen in recent experiments.

arXiv comment14 pages, including 4 pages of appendices, 4 figures. Companion paper: arXiv:2202.10366

References in corpus (29)

• Cuba - a library for multidimensional numerical integration
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Theory of Thermal Hall Effect in Quantum Magnets
• Topological Nature of the Phonon Hall Effect
• Rotational motion of magnon and thermal Hall effect
• Fractional excitations in the square-lattice quantum antiferromagnet
• Berry Curvature and Phonon Hall Effect
• Giant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates
• Phonons become chiral in the pseudogap phase of cuprates
• Theory of Phonon Hall Effect in Paramagnetic Dielectrics
• Phonon thermal Hall effect in strontium titanate
• Thermal Hall Effect Induced by Magnon-Phonon Interactions
• Quantum dynamics and entanglement of spins on a square lattice
• Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectric
• Thermal Hall conductivity in the cuprate Mott insulators Nd${}_2$CuO${}_4$ and Sr${}_2$CuO${}_2$Cl${}_2$
• Enhanced thermal Hall effect in nearly ferroelectric insulators
• Origin of the Phonon Hall Effect in Rare-Earth Garnets
• Berry phase of phonons and thermal Hall effect in nonmagnetic insulators
• Large Phonon Thermal Hall Conductivity in a Simple Antiferromagnetic Insulator
• Chirality-driven Hall Transport Phenomena of Spins
• Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study
• Charged Defects and Phonon Hall Effects in Ionic Crystals
• Consideration of Thermal Hall Effect in Undoped Cuprates
• Extrinsic phonon thermal Hall transport from Hall viscosity
• Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system
• Phonon Hall viscosity from phonon-spinon interactions
• Large extrinsic phonon thermal Hall effect from resonant scattering
• Thermal Conductivity and Theory of Inelastic Scattering of Phonons by Collective Fluctuations
• Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces

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