  Hard-core/soft shell (HCSS) particles have been shown to self-assemble into a
remarkably rich variety of structures under compression due to the simple
interplay between the hard-core and soft-shoulder length scales in their
interactions. Most studies in this area model the soft shell interaction as a
square shoulder potential. Although appealing from a theoretical point of view,
the potential is physically unrealistic because there is no repulsive force in
the soft shell regime, unlike in experimental HCSS systems. To make the model
more realistic, here we consider HCSS particles with a range soft shell
potential profiles beyond the standard square shoulder form and study the model
using both minimum energy calculations and Monte Carlo simulations. We find
that by tuning density and the soft shell profile, HCSS particles in the thin
shell regime (i.e., shell to core ratio $r_1/r_0 \leq \sqrt{3}$) can form a
large range of structures, including hexagons, chains, squares, rhomboids and
two distinct zig-zag structures. Furthermore, by tuning the density and
$r_1/r_0$, we find that HCSS particles with experimentally realistic linear
ramp soft shoulder repulsions can form honeycombs and quasicrystals with
10-fold and 12-fold symmetry. Our study therefore suggests the exciting
possibility of fabricating these exotic 2D structures experimentally through
colloidal self-assembly.
