Twisted smectics as the liquid crystal analogues of type II superconductors

Abstract

In 1972, de Gennes pointed out the formal analogy between the Landau–Ginzburg Hamiltonians describing the phase transition from normal to superconductor on one hand and from nematic to smectic A liquid crystals on the other hand. This elegant analogy became a source of inspiration not only for theoreticians, as it revealed and emphasised the beauty and the richness of the physics of liquid crystals, but also for chemists in their constant search for novel liquid crystalline structures. The analogy with type I superconductors was first described and bore an appropriate educational value: the expulsion of twist in smectic liquid crystals can be viewed as equivalent to the well-known Meissner effect in superconductors. However, the investigation of the type II condition definitely opened new doors as it led to the discovery of fantastic new liquid crystal structures. In 1988, Renn and Lubensky ‘invented’ the Twist Grain Boundary (TGB) smectic phase as the direct analogue of the Abrikosov flux lattice. The twist penetrates the smectic layers of a TGB via a twisted lattice of screw dislocations analogous to magnetic vortices, just as the magnetic field penetrates the type II superconductor. We review in this paper the major steps of the experimental studies of the TGB phases and show that the observed behaviours closely follow the superconductor model, hence illustrating the depth of de Gennes' analogy.