Dielectric permittivity of ultrathin PbTiO3 nanowires from first principles

We propose an efficient method to compute the dielectric permittivity of nanostructures by combining first principles density functional perturbation theory with effective medium theory. Specifically, ultrathin axially symmetric ferroelectric PbTiO3 nanowires are considered. As established previously by Pilania and Ramprasad (Phys Rev B 82:155442, 2010), (4 × 4) PbO-terminated nanowire and (4 × 4) TiO2-terminated nanowire display, respectively, a uniform axial and a vortex polarization in their ground state configurations (the latter with a non-zero axial toroidal moment). Both nanowires, regardless of the lateral surface termination, display a significantly larger dielectric constant value along the axial direction, and diminished values along the off-axis directions, as compared to the corresponding bulk values. Our results further suggest that the nanowires with unconventional vortex-type polarization states are expected to have an increased dielectric response as compared to those with conventional uniform axial polarization. The method proposed here is quite general and readily extendable to other zero-, one-, and two-dimensional nanostructures.