  We predict theoretically that the motion of a polar crystalline layer between
two graphene planes exerts Coulomb drag on electrons in graphene, inducing a
DC-drag current. The physical mechanism of this drag relies on the intervalley
scattering of charge carriers in graphene by the time-dependent potential of
the moving crystalline layer. The drag current exhibits a nonlinear Hall
effect, which can be used for the experimental measurement of the Berry
curvature. In turn, the drag of electrons in graphene exerts a back-action on
the crystalline layer, which can be expressed in terms of increased dynamic
viscosity.
