Evidence for a Berezinskii-Kosterlitz-Thouless phase in ferroelectric thin-films*

The Berezinskii-Kosterlitz-Thouless ($\mathsf{BKT}$) theory, discovered more than 40 years ago, has propelled the notion of topological phase transition, and has a venerable history and a seminal impact upon condensed matter physics and other areas in physics. So far, the question of whether low-dimensional ferroelectrics would manifest $\mathsf{BKT}$ physics has been eluded. Our work aims at bridging this gap as it focuses on the investigation of the critical properties of ferroelectric thin-films, namely BaTiO$_3$ under tensile strain. Using Monte Carlo simulations of a first-principles-based effective Hamiltonian scheme as well as scaling, symmetry, and topological arguments, we find that an intermediate critical $\mathsf{BKT}$ phase underlain by quasi-continuous symmetry emerges between the ferroelectric phase and the disordered paraelectric one. This overlooked intermediate phase supports quasi-long-range order reflected in the algebraic decay of the correlation function and sustained by the existence of neutral bound pairs of vortices and antivortices, in accordance with defining characteristics of a $\mathsf{BKT}$ phase. Our results therefore highlight the subtle, fundamental richness of low-dimensional ferroelectrics and widen the realm of $\mathsf{BKT}$ transitions.