  Angular momentum conversion between mechanical rotation and the valley degree
of freedom in 2D Dirac materials is investigated theoretically. Coupling
between the valley and vorticity of dynamic lattice distortions is derived by
applying the k.p method to 2D Dirac materials with an inertial effect. Lattice
strain effects are also incorporated. Valley transfer and valley-dependent
carrier localization are predicted using the dynamic lattice distortions. The
transport properties are found to be controllable, allowing the system to be
insulating and to generate pulsed charge current. Our formalism offers a route
toward mechanical manipulation of valley dynamics in 2D Dirac materials.
