Lattice dynamics with molecular Berry curvature: chiral optical phonons

TL;DR

This paper explores how molecular Berry curvature influences lattice dynamics, leading to chiral optical phonons with circular polarization and intrinsic degeneracy lifting in systems with broken time-reversal symmetry.

Contribution

It introduces a formulation of molecular Berry curvature affecting lattice dynamics and demonstrates its impact on phonon polarization and degeneracy lifting in the Haldane model.

Findings

Large molecular Berry curvature near the Brillouin zone center.

Degeneracy of optical phonons is intrinsically lifted.

Optical phonons exhibit circular polarization and large Berry curvature.

Abstract

Under the Born-Oppenheimer approximation, the electronic ground state evolves adiabatically and can accumulate geometrical phases characterized by the molecular Berry curvature. In this work, we study the effect of the molecular Berry curvature on the lattice dynamics in a system with broken time-reversal symmetry. The molecular Berry curvature is formulated based on the single-particle electronic Bloch states. It manifests as a non-local effective magnetic field in the equations of motion of the ions that are beyond the widely adopted Raman spin-lattice coupling model. We employ the Bogoliubov transformation to solve the quantized equations of motion and to obtain phonon polarization vectors. We apply our formula to the Haldane model on a honeycomb lattice and find a large molecular Berry curvature around the Brillouin zone center. As a result, the degeneracy of the optical branches at this point is lifted intrinsically. The lifted optical phonons show circular polarizations, possess large phonon Berry curvature, and have a nearly quantized angular momentum that modifies the Einstein-de Haas effect.