Covariant elasticity and dislocations in smectic-Cliquid crystals

We derive a rotationally invariant form for the elastic energy of a smectic-C liquid crystal. The magnitude of the c director, but not its direction, can screen layer strain just as two independent components of the director screen strain in smectic-A liquid crystals. Type I and type II smectic-C liquid crystals can be classified according to whether the c-director penetration depth ${\lambda }_{\mathit{c}}$ is less than or greater than the smectic coherence length ξ. We calculate the energies of isolated dislocations and the interaction energies of parallel dislocations as a function of direction. We find an attractive interaction at large distances between like-sign screw dislocations and a repulsive interaction at short distances, leading to a minimum energy separation. (c) 1995 The American Physical Society