  In many cases, the stability of complex structures in colloidal systems is
enhanced by a competition between different length scales. Inspired by recent
experiments on nanoparticles coated with polymers, we use Monte Carlo
simulations to explore the types of crystal structures that can form in a
simple hard-core square shoulder model which explicitly incorporates two
favored distances between the particles. To this end, we combine Monte
Carlo-based crystal structure finding algorithms with free energies obtained
using a mean-field cell theory approach, and draw phase diagrams for two
different values of the square shoulder width as a function of the density and
temperature. Moreover, we map out the zero-temperature phase diagram for a
broad range of shoulder widths. Our results show the stability of a rich
variety of crystal phases, such as body-centered orthogonal (BCO) lattices, not
previously considered for the square shoulder model.
