Absence of Ferroelectric Critical Size in Ultrathin PbTiO3 Nanotubes: A Density-Functional Theory Study

We simulate from first principles the energetic, structural, and electronic properties of ferroelectric (FE) ultrathin PbTiO3 nanotubes. The nanotube possesses spontaneous polarization despite their sidewalls being thinner than the critical thickness at which the thin films lose ferroelectricity; this indicates the absence of an intrinsic critical size for ferroelectricity. The ground state of the nanotube is not purely FE since it primarily involves antiferrodistortive (AFD) rotations of oxygen atoms due to compression in the inner tube wall. The emergence of the AFD displacement plays a central role in stabilizing both the nanotubular structure and FE distortions due to direct AFD-FE coupling. Moreover, we predict intriguing rich phase transitions due to axial strains including polarization vortices as an important class of nanoscale FE ordering.