  The celebrated Berezinskii-Kosterlitz-Thouless (BKT) phase transition refers
to a topological transition characterized, e.g., by the dissociation of
vortex-antivortex pairs in two-dimensional (2D) systems. Such unusual phase has
been reported in various types of materials, but never in the new class of
systems made by one-unit-cell-thick (1UC) ferroelectrics (also coined as 2D
ferroelectrics). Here, the use of a first-principles-based effective
Hamiltonian method leads to the discovery of many fingerprints of a BKT phase
existing in-between the ferroelectric and paraelectric states of 1UC tin
tellurium being fully relaxed. Moreover, epitaxial strain is found to have
dramatic consequences on the temperature range of such BKT phase for the 1UC
SnTe. Consequently, our predictions extend the playground of BKT theory to a
novel class of functional materials, and demonstrate that strain is an
effective tool to alter BKT characteristics there.
