  It is shown that an electric field applied to p-doped graphane generates a
dissipationless orbital momentum Hall current. In the clean limit the
corresponding Hall conductivity is independent of the concentration of holes.
The Hall effect is related to the $2\pi$-Berry phase accumulated when heavy and
light holes are transported around the degeneracy point in the center of the
Brillouin zone. This also leads to the orbital momentum edge currents in the
equilibrium state, and to the accumulation of the orbital momentum at the edges
when the system is driven out of equilibrium.
