  In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero
local Berry curvature of low-energy massive Dirac fermions can give rise to
nontrivial spin and charge responses, even though the integral of the Berry
curvature over all occupied states is zero. In this work, we present a new
effect induced by the electronic Berry curvature. By studying electron-phonon
interactions in BaMnSb$_2$, a prototype two-dimensional Dirac material
possessing two TR-related massive Dirac cones, we find that the nonzero local
Berry curvature of electrons can induce a phonon angular momentum. The
direction of this phonon angular momentum is locked to the phonon propagation
direction, and thus we refer it as "phonon helicity", in a way that is
reminiscent of electron helicity in spin-orbit-coupled electronic systems. We
discuss possible experimental probes of such phonon helicity.
