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We introduce a one-parameter family, $0 \leq H \leq 1$, of pair potentialfunctions with a single relative energy minimum that stabilize a range ofvacancy-riddled crystals as ground states. The "quintic potential" is ashort-ranged, nonnegative pair potential with a single local minimum of height$H$ at unit distance and vanishes cubically at a distance of $\rt$. We havedeveloped this potential to produce ground states with the symmetry of thetriangular lattice while favoring the presence of vacancies. After anexhaustive search using various optimization and simulation methods, we believethat we have determined the ground states for all pressures, densities, and $0\leq H \leq 1$. For specific areas below $3\rt/2$, the ground states of the"quintic potential" include high-density and low-density triangular lattices,kagom\'{e} and honeycomb crystals, and stripes. We find that these groundstates are mechanically stable but are difficult to self-assemble in computersimulations without defects. For specific areas above $3\rt/2$, these systemshave a ground-state phase diagram that corresponds to hard disks with radius$\rt$. For the special case of H=0, a broad range of ground states isavailable. Analysis of this case suggests that among many ground states, ahigh-density triangular lattice, low-density triangular lattice, and stripedphases have the highest entropy for certain densities. The simplicity of thispotential makes it an attractive candidate for experimental realization withapplication to the development of novel colloidal crystals or photonicmaterials.

Novel Ground-State Crystals with Controlled Vacancy Concentrations: From Kagom\'{e} to Honeycomb to Stripes