  We study numerically the optical properties of low-buckled silicene and
AB-stacked bilayer graphene quantum dots subjected to an external electric
field, which is normal to their surface. Within the tight-binding model, the
optical absorption is calculated for quantum dots, of triangular and hexagonal
shapes, with zigzag and armchair edge terminations. We show that in triangular
silicene clusters with zigzag edges a rich and widely tunable infrared
absorption peak structure originates from transitions involving zero energy
states. The edge of absorption in silicene quantum dots undergoes red shift in
the external electric field for triangular clusters, whereas blue shift takes
place for hexagonal ones. In small clusters of bilayer graphene with zigzag
edges the edge of absorption undergoes blue/red shift for triangular/hexagonal
geometry. In armchair clusters of silicene blue shift of the absorption edge
takes place for both cluster shapes, while red shift is inherent for both
shapes of the bilayer graphene quantum dots.
