  Most theoretical descriptions of lyotropic cholesteric liquid crystals to
date focus on homogeneous systems in which the rod concentration, as opposed to
the rod orientation, is uniform. In this work, we build upon the
Onsager-Straley theory for twisted nematics and study the effect of weak
concentration gradients, generated by some external potential, on the
cholesteric twist. We apply our theory to chiral nematics of nanohelices in
which the supramolecular helix sense is known to spontaneously change sign upon
variation of particle concentration, passing through a so-called compensation
point at which the mesoscopic twist vanishes. We show that the imposed field
offers exquisite control of the handedness and magnitude of the helicoidal
director field, even at weak field strengths. Within the same framework we also
quantify the director fluctuation spectrum and find evidence for a correlation
length diverging at the compensation point.
