  The intrinsic spin and valley Hall conductivities of silicene, germanene and
other similar two dimensional crystals are explored theoretically. Particular
attention is given to the effects of the intrinsic spin-orbit coupling,
electron doping and the type of insulating phase of the system (i.e., a
topological insulator or a band insulator) which can be tuned by a
perpendicular electric field. At finite frequency, the transverse edge to which
carriers of particular spin and valley label flow can be controlled such that
an accumulation of a particular combination of spin and valley index can be
obtained. The direction of flow is found to be dependent on the type of
insulating phase. The magnitude of the Hall conductivity response is enhanced
from the DC values at certain incident photon frequencies associated with the
onset of interband transitions. Analytic results are presented for both the DC
and finite frequency results.
