  Surface properties are examined in a chiral d-wave superconductor with
hexagonal symmetry, whose one-body Hamiltonian possesses the intrinsic
spin-orbit coupling identical to the one characterizing the topological nature
of the Kane-Mele honeycomb insulator. In the normal state spin-orbit coupling
gives rise to spontaneous surface spin currents, whereas in the superconducting
state there exist besides the spin currents also charge surface currents, due
to the chiral pairing symmetry. Interestingly, the combination of these two
currents results in a surface spin polarization, whose spatial dependence is
markedly different on the zigzag and armchair surfaces. We discuss various
potential candidate materials, such as SrPtAs, which may exhibit these surface
properties.
