MULTICRITICAL BEHAVIOR OF ABRIKOSOV VORTEX LATTICES NEAR THE CHOLESTERIC SMECTIC-A SMECTIC-C-STAR POINT

The mean-field phase diagram of the cholesteric-smectic-A-smectic-C* (N*-Sm-A-Sm-C*) point is derived within the framework of the chiral Chen-Lubensky model. We show that on the Sm-C* side of the phase diagram, one or two additional twist-grain-boundary (TGB) (or chiral-smectic) phases will occur. These additional chiral-smectic phases, the TGB(C) and TGB(C)* phases, are highly dislocated versions of smectic-C and smectic-C* phases, respectively. According to the de Gennes superconductor analogy, the grain-boundary phase which occurred on the smectic-A side of the phase diagram (known as the TGB(A) or chiral Sm-A*) is the analog of the Abrikosov vortex lattice in type-II superconductors. However, the TGB(C) and TGB(C*) phases would correspond to Abrikosov vortex lattices in a hypothetical superconductor where the Ginzburg parameter K is negative and the photon has Bose condensed. These additional phases are predicted to occur near the recently observed N*-Sm-A*-Sm-C* multicritical point. We discuss the N*-TGB(C), TGB(A)-TGB(C), and TGB(A)-TGB(C*) phase transitions. Because of the twist, the XY-like Sm-A-Sm-C is (usually) replaced by the Ising-like TGB(A)-TGB(C). However, if the Sm-C* helicoidal pitch length is somewhat smaller than the cholesteric pitch length, then the TGB(A)-TGB(C) transition would be replaced by the TGB(A)-TGB(C*) transition.