  Chirality is a recurrent theme in the study of biological systems, in which
active processes are driven by the internal conversion of chemical energy into
work. Bacterial flagella, acto-myosin filaments and microtubule bundles are
active systems which are also intrinsically chiral. Despite some exploratory
attempt to capture the relations between chirality and motility, no
intrinsically chiral system has ever been analyzed so far. To address this gap
in knowledge, here we study the effects of internal active forces and torques
on a three-dimensional droplet of cholesteric liquid crystal (CLC) embedded in
an isotropic liquid. We consider tangential anchoring of the liquid crystal
director at the droplet surface. Contrary to what happens in nematics, where
moderate extensile activity leads to droplet rotation, cholesteric active
droplets exhibit a lot more complex and variegated behaviors. We find that
extensile force dipole activity stabilises complex defect configurations whose
orbiting dynamics couples to thermodynamic chirality to propel screw-like
droplet motion. Instead, dipolar torque activity may either tighten or unwind
the cholesteric helix, and if tuned can power rotations with an oscillatory
angular velocity of zero mean.
