  We study elastic interactions between colloidal particles and deformation
landscapes of undulations in a cholesteric liquid crystal under an electric
field applied normal to cholesteric layers. The onset of undulation instability
is influenced by the presence of colloidal inclusions and, in turn, layers'
undulations mediate the spatial patterning of particle locations. We find that
the bending of cholesteric layers around a colloidal particle surface prompts
the local nucleation of an undulations lattice at electric fields below the
well-defined threshold known for liquid crystals without inclusions, and that
the onset of the resulting lattice is locally influenced, both dimensionally
and orientationally, by the initial arrangements of colloids defined using
laser tweezers. Spherical particles tend to spatially localize in the regions
of strong distortions of the cholesteric layers, while colloidal nanowires
exhibit an additional preference for multistable alignment offset along various
vectors of the undulations lattice. Magnetic rotation of superparamagnetic
colloidal particles couples with the locally distorted helical axis and
undulating cholesteric layers in a manner that allows for a controlled
three-dimensional translation of these particles. These interaction modes lend
insight into the physics of liquid crystal structure-colloid elastic
interactions, as well as point the way towards guided self-assembly of
reconfigurable colloidal composites with potential applications in diffraction
optics and photonics.
