  Silicene systems, due to the buckled structure of the lattice, manifest
remarkable intrinsic spin-orbit interaction triggering a topological phase
transition in the low-energy regime. Thus, we found that protected edge states
are present in silicene antidots and dots, being polarized in valley-spin
pairs. We have also studied the effect of the lattice termination on the
properties of the single electron energy levels and electron density
distribution of silicene antidots and dots situated in a perpendicular magnetic
field. Our calculations confirmed that the topological edge states are
propagating over the perimeter of the antidot/dot for both ideal or realistic
edge termination containing roughness on the atomic length scale. The valley
polarization and the slope of the energy line as a function of the magnetic
field is, however, reduced when the antidot or dot has a rough edge.
