Phonon angular momentum and chiral phonons
Authors: Yu Hang  , Xu Xi-Fang  , Niu Qian  , Zhang Li-Fa  ,   School of Physics and Technology, Nanjing Normal University, Nanjing 210000, China;,   Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
Published: December 2020

In traditional physics, phonon is widely regarded as being linearly polarized, which means that phonon carries zero angular momentum. Thus the angular momentum of lattice related to mechanical rotation only reflects the lattice rigid-body motion. Recently, in a magnetic system with time reversal symmetry broken by spin-phonon interaction, one found that the phonon angular momentum is nonzero and an odd function of magnetization. At zero temperature, phonon was reported to have a zero-point angular momentum and zero-point energy. Thus the gyromagnetic ratio obtained through the Einstein-de Haas effect needs correcting by considering the nonzero phonon angular momentum. As is well known, if phonon has nonzero angular momentum, which means that phonon can have rotation, it can be right-handed or left-handed, that is, the phonon is chiral. Actually, we can define the polarization of phonon to represent the phonon chirality, which comes from the circular vibration of sublattices. When the phonon polarization is larger (less) than zero, the phonon is right (left)-handed. In non-magnetic honeycomb AB lattices, with inversion symmetrybrocken, the chiral phonons are found to be of valley contrasting circular polarization and concentrated in Brillouin-zone corners. At valleys, there is a three-fold rotational symmetry endowing phonons with quantized pseudo angular momentum. Then conversation of pseudo angular momentum, which determines the selection rules in phonon-involved intervalley scattering of electrons, must be satisfied. Chiral valley phonons can be measured by polarized infrared absorption or emission. In addition, since the phonon Berry curvature is reported to be nonzero at valley, it can distort phonon transport under a strain gradient, which can act as an effective magnetic field. Thus, a valley phonon Hall effect is theoretically predicted, which is probably a method of measuring chiral valley phonons. In consideration of phonons angular momentum and chiral phonons, photon helicity changed by phonons at Gamma point will be explained reasonably. In conclusion, chiral phonons are present in systems that break time reversal or spatial inversion symmetries. In a magnetic system, where time reversal symmetry is broken, phonons generally carry a nonzero angular momentum, which can influence the classic Einstein-de Haas effect. In a nonequilibrium system, the phonon Hall effect can be observed due to the chiral phonons. In a non-magnetic crystal, with inversion symmetry brocken, phonons in the Brillouin-zone center and corners are chiral and have a quantized pseudo angular momentum, providing an alternative to valleytronics in insulators. We believe that the findings of the phonon angular momentum and the chiral phonons together with phonon pseudoangular momentum, selection rules, and valley phonon Hall effect will lead to the relevant exploration and new development of phonon related subject in condensed matter physics.