Berezinskii-Kosterlitz-Thouless phases in ultra-thin PbTiO$_3$/SrTiO$_3$ superlattices

TL;DR

This study demonstrates the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in ultra-thin PbTiO3/SrTiO3 superlattices through simulations, revealing a temperature range with quasi-long-range order and vortex-antivortex pairs, and suggests experimental feasibility.

Contribution

First simulation-based evidence of BKT phases in ferroelectric superlattices, highlighting the role of strain and boundary conditions in stabilizing these topological phases.

Findings

BKT phase exists between ordered ferroelectric and disordered paraelectric phases.

Quasi-long-range order characterized by power-law decay of correlations.

Presence of vortex-antivortex pairs influenced by temperature.

Abstract

We study the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in (PbTiO$_3$)$_3$/(SrTiO$_3$)$_3$ superlattices by means of second-principles simulations. Beyond a threshold tensile epitaxial strain of $\epsilon = 0.25 \%$ 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 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 $T_{\rm BKT}$. 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 bounded vortex-antivortex pairs whose density is determined by a thermal activation process. The proposed PbTiO$_{3}$/SrTiO$_{3}$ superlattice model and the imposed mechanical boundary conditions are both experimentally feasible, opening the door for the first experimental observation of these new topological phases in ferroelectric materials.