  Chiral crystals consisting of micro-helices have many optical properties
while presently available fabrication processes limit their large-scale
applications in photonic devices. Here, by using a simplified simulation
method, we investigate a bottom-up self-assembly route to build up helical
crystals from the smectic monolayer of colloidal helices racemate. With
increasing the density, the system undergoes an entropy-driven
co-crystallization by forming crystals of various symmetries with different
helical shapes. In particular, we identify two crystals of helices arranged in
the binary honeycomb and square lattices, which are essentially composed by two
sets of opposite-handed chiral crystal. Photonic calculations show that these
chiral structures can have large complete photonic bandgaps. In addition, in
the self-assembled chiral square crystal, we also find dual polarization
bandgaps that selectively forbid the propagation of circularly polarized lights
of a specific handedness along the helical axis direction. The self-assembly
process in our proposed system is robust, suggesting possibilities of using
chiral colloids to assemble photonic metamaterials.
