  We study graphene which has both spin-orbit coupling (SOC), taken to be of
the Kane-Mele form, and a Zeeman field induced due to proximity to a
ferromagnetic material. We show that a zigzag interface of graphene having SOC
with its pristine counterpart hosts robust chiral edge modes in spite of the
gapless nature of the pristine graphene; such modes do not occur for armchair
interfaces. Next we study the change in the local density of states (LDOS) due
to the presence of an impurity in graphene with SOC and Zeeman field, and
demonstrate that the Fourier transform of the LDOS close to the Dirac points
can act as a measure of the strength of the spin-orbit coupling; in addition,
for a specific distribution of impurity atoms, the LDOS is controlled by a
destructive interference effect of graphene electrons which is a direct
consequence of their Dirac nature. Finally, we study transport across junctions
which separates spin-orbit coupled graphene with Kane-Mele and Rashba terms
from pristine graphene both in the presence and absence of a Zeeman field. We
demonstrate that such junctions are generally spin active, namely, they can
rotate the spin so that an incident electron which is spin polarized along some
direction has a finite probability of being transmitted with the opposite spin.
This leads to a finite, electrically controllable, spin current in such
graphene junctions. We discuss possible experiments which can probe our
theoretical predictions.
