  We consider a square lattice configuration of circular gate-defined quantum
dots in an unbiased graphene sheet and calculate the electronic, particularly
spectral properties of finite albeit actual sample sized systems by means of a
numerically exact kernel polynomial expansion technique. Analyzing the local
density of states and the momentum resolved photoemission spectrum we find
clear evidence for a series of quasi-bound states at the dots, which can be
probed by optical measurements. We further analyze the interplay of the
superlattice structure with dot localized modes on the electron energy
dispersion. Effects of disordered dot lattices are discussed too.
