title: 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-Hermitian 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 the 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 wavevector space of the kagome lattice.
authors.affiliation: Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore.
authors.forename: Lifa
authors.initials: L
authors.lastname: Zhang
authors.forename: Jie
authors.initials: J
authors.lastname: Ren
authors.forename: Jian-Sheng
authors.initials: JS
authors.lastname: Wang
authors.forename: Baowen
authors.initials: B
authors.lastname: Li