We study the equilibrium arrangements of polarization vortices in (${\mathrm{PbTiO}}_3{)}_n/({\mathrm{SrTiO}}_3{)}_n$ superlattices by means of second-principles simulations. We find that, at low temperatures, polarization vortices organize in a regular arrangement in which clockwise and counterclockwise vortices alternate positions, leading to a crystal-like structure with well-defined handedness. This chiral crystal melts at a critical temperature $T_{\mathrm{M}}$ into a chiral liquid where long-range order is lost but handedness is preserved. At even higher temperatures $T_{\mathrm{C}}$, 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.

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• Ferroelectricity
• First-principles calculations
• Structural order parameter
• Topological materials