Berezinskii-Kosterlitz-Thouless phases in ultrathin PbTiO3/SrTiO3 superlattices

We study the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in ${({\mathrm{PbTiO}}_{3})}_{3}/{({\mathrm{SrTiO}}_{3})}_{3}$ superlattices by means of second-principles simulations. Between a tensile epitaxial strain of $\ensuremath{\epsilon}=0.25--1\phantom{\rule{0.16em}{0ex}}%$, the local dipole moments within the superlattices are confined to the film-plane, and thus the polarization can be effectively considered as two-dimensional. The analysis of the decay of the dipole-dipole correlation with the distance, together with the study of the density of defects and its distribution as a function of temperature, supports the existence of a BKT phase in a range of temperature mediating the ordered ferroelectric (stable at low $T$), and the disordered paraelectric phase that appears beyond a critical temperature ${T}_{\mathrm{BKT}}$. This BKT phase is characterized by quasi-long-range order (whose signature is a power-law decay of the correlations with the distance), and the emergence of tightly bound vortex-antivortex pairs whose density is determined by a thermal activation process. The proposed ${\mathrm{PbTiO}}_{3}/{\mathrm{SrTiO}}_{3}$ superlattice model and the imposed mechanical boundary conditions are both experimentally feasible, making it susceptible for an experimental observation of these new topological phases in ferroelectric materials.