The phonon Hall effect: theory and application

Abstract

We present a systematic theory of the phonon Hall effect in a ballistic crystal lattice system, and apply it on the kagome lattice which is ubiquitous in various real materials. By proposing a proper second quantization for the non-Hermite Hamiltonian in the polarization-vector space, we obtain a new heat current density operator with two separate contributions: the normal velocity responsible for the longitudinal phonon transport, and the anomalous velocity manifesting itself as the Hall effect of transverse phonon transport. As exemplified in kagome lattices, our theory predicts that the direction of Hall conductivity at low magnetic field can be reversed by tuning temperatures, which we hope can be verified by experiments in the future. Three phonon-Hall-conductivity singularities induced by phonon-band-topology change are discovered as well, which correspond to the degeneracies at three different symmetric center points, Γ, K, X, in the wave-vector space of the kagome lattice.

19 pages, 6 figures

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• Valley contrasting chiral phonons in monolayer hexagonal lattices
• Topological Magnon Insulator in Insulating Ferromagnet
• Angular Momentum of Phonons and Einstein-de Haas Effect
• Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators
• Berry Curvature and Phonon Hall Effect
• Hall effect of triplons in a dimerized quantum magnet
• Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations
• Phono-magnetic analogs to opto-magnetic effects
• Origin of the Phonon Hall Effect in Rare-Earth Garnets
• Topological Magnetoelastic Excitations in Non-Collinear Antiferromagnets
• Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
• Topological Edge Modes by Smart Patterning
• Charged Defects and Phonon Hall Effects in Ionic Crystals
• Magnonic Analogs of Topological Dirac Semimetals
• p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet
• Classification of materials with phonon angular momentum and microscopic origin of angular momentum
• Thermal Hall effect incorporating magnon damping in localized spin systems
• Nonlinear phonon Hall effects in ferroelectrics: its existence and non-volatile electrical control
• Topological band structure of surface acoustic waves on a periodically corrugated surface
• Electric field induced thermal Hall effect of triplons in the quantum dimer magnets $X$CuCl${}_3$ ($X=$ Tl, K)
• Multipolar edge states in the breathing kagome model
• Chiral phonons in binary compounds $A$Bi ($A$ = K, Rb, Cs) with P2${}_1$/c structure
• Nernst-like Effect in a Flexible Chain
• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices
• Topological hard-core bosons on the honeycomb lattice
• Chiral Phonons Arising From Chirality-Selective Magnon-Phonon Coupling