Melting of Crystals of Polarization Vortices and Chiral Phase Transitions in Oxide Superlattices

We study the equilibrium arrangements of polarization vortices in (PbTiO_3)_n/(SrTiO_3)_n superlattices by means of second-principles simulations. We find that, at low temperatures, polarization vortices organize in a regular arrangement in which clockwise and counter-clockwise vortices alternate positions, leading to a crystal-like structure with well defined handedness. This chiral crystal melts at a critical temperature T_M into a chiral liquid, where long-range order is lost but handedness is preserved. At even higher temperatures, T_C, a second phase transition occurs, at which the chiral liquid of polarization vortices loses its handedness. Both phase transitions can be readily identified by the adequate choices of order parameters.