Phase transition between the cholesteric and twist grain boundary $C$ phases

The upper critical temperature $T_{c2\mathrm{}}$ for the phase transition between the cholesteric phase ${(N}^{*})$ and the twist grain boundary $C$ phase with the layer inclination tilted to the pitch axis $\left({\mathrm{TGB}}_{\mathrm{Ct}}\right)$ in thermotropic liquid crystals is determined by the mean field Chen-Lubensky approach. We show that the $N^{*}-{\mathrm{TGB}}_{\mathrm{Ct}}$ phase transition is split in two with the appearance of either the ${\mathrm{TGB}}_A$ or the ${\mathrm{TGB}}_{2q}$ phase in a narrow temperature interval below $T_{c2\mathrm{}}$. The latter phase is novel in being superposed from two degenerate ${\mathrm{TGB}}_{\mathrm{Ct}}$ phases with different (left and right) layers inclinations to the pitch axis.