Berezinskii– Kosterlitz–Thouless phase transitions in PbTiO$_3$/SrTiO$_3$ superlattices*

It is well known that two dimensional systems with continuous symmetries and short-range interactions, in the absence of symmetry breaking mechanisms, can undergo topological phase transitions driven by the unbinding of local defects pairs [1].

Moreover, it has been proven that these type of transitions can appear in ferroelectrics mediating between their low-symmetry and high-symmetry phases when the order parameter is restricted within a plane [2,3].

Using second-principles methods as implemented in the SCALE-UP code [4] we study the possibility of finding these type of transitions in PbTiO$_3$/SrTiO$_3$ superlattices when the order parameter is allowed to escape to the third dimension forming vortices in the polar structures [5].
[1] J. M. Kosterlitz and D. J. Thouless, J. Phys. C 5, L124 (1972)
[2] Y. Nahas et al., Phys. Rev. Lett. 119, 117601 (2017)
[3] C. Xu et al., Phys. Rev. B 101 241402 (2020)
[4] P. García-Fernández et al., Phys. Rev. B 93 195137 (2016)
[5] P. Shafer et al., PNAS 115, 915 (2018)