Atomistic theory of the phonon angular momentum Hall effect

Abstract

The spin and orbital Hall effects convert longitudinal charge currents into transverse flows of electronic angular momentum. Here we develop an atomistic theory of the recently proposed lattice-vibrational analogue, in which a longitudinal heat current driven by a thermal gradient is converted into a transverse current of phonon angular momentum. We derive a microscopic real-space expression for this current and show that it originates from thermally induced mixing of polarized vibrational motion, leading to a characteristic edge accumulation of phonon angular momentum. We demonstrate the effect in minimal square- and honeycomb-lattice models and compute the resulting phonon angular momentum accumulations for a range of example materials using input from first-principles calculations. Our results confirm that the phonon angular momentum Hall effect is a universal response of crystalline solids and our framework is generically applicable to all materials.