The phonon Hall effect: theory and application

TL;DR

This paper develops a comprehensive theoretical framework for the phonon Hall effect in crystal lattices, demonstrating how magnetic fields and temperature tuning influence phonon transport and revealing topological singularities in kagome lattices.

Contribution

It introduces a novel second quantization approach for non-Hermite Hamiltonians and predicts tunable Hall conductivity and topological phonon phenomena in kagome lattices.

Findings

Hall conductivity direction can be reversed by temperature tuning.

Three singularities in phonon Hall conductivity linked to band topology.

Theoretical predictions applicable to real kagome materials.

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, \Gamma, K, X, in the wave-vector space of the kagome lattice.