Collective Interference of Phonon Spin and Dipole Moment Rotation Induced Circular Dichroism

Abstract

The classical field description of phonon spin relies on the invariance of a continuous elastic field under infinitesimal rotation. However, a local medium element in the continuous field may contain large numbers of vibrational particles at microscopic level, like for complex lattices with many atoms in a unit cell. We find this causes the phonon spin in real materials no longer a simple sum of each atom rotation, but a collective interference of many atoms, since phonons are phase-coherent vibrational modes across unit cells. We demonstrate the collective interference phonon spin manifested as the dipole moment rotating (DMR) of charge-polarized unit cell, by deriving the infrared circular dichroism (ICD) with phonon-photon interaction in complex lattices. We compare the DMR with the local atom rotation without interference, and exemplify their distinct ICD spectrum in a chiral lattice model and two realistic chiral materials. Detectable ICD measurements are proposed in quartz with Weyl phonon near Gamma point. Our study underlies the important role of collective interference and uncovers a deeper insight of phonon spin in real materials with complex lattices.