Crystal-Liquid phase transition of polarization curl density in PbTiO$_3$/SrTiO$_3$ superlattices*

Recent studies of the temperature evolution of the polarization patterns in oxide superlattices shows complex behaviour [1-3] different from the classical ferro/paraelectric phase transitions where the polarization is the relevant order parameter to track.

Using second-principles methods as implemented in the Scale-UP [4] code we report a first-order crystal-liquid like temperature-driven phase transition in (PbTiO$_3$)$_n$/(SrTiO$_3$)$_n$ superlattices in which the relevant order parameter is related with the curl density of the polarization pattern. Different values of the perioditiy $n=8,~10,~14$ were studied showing good scaling for the phase transition. 

[1] Y. Nahas, et al., Phys. Rev. Lett. 119, 117601 (2017)

[2] C. Xu, et al., Phys. Rev. B. 101, 241402 (2020)

[3] Y. Nahas, et al., Nature 577, 47–51 (2020)

[4] P. Garc\'ia-Fern\'andez, et al., Phys. Rev. B 93 195137 (2016)