  Polar chiral structures have recently attracted much interest within the
scientific community, as they pave the way towards innovative device concepts
similar to the developments achieved in nanomagnetism. Despite the growing
interest, many fundamental questions related to the mechanisms controlling the
appearance and stability of ferroelectric topological structures remain open.
In this context, ferroelectric nanoparticles provide a flexible playground for
such investigations. Here, we present a theoretical study of ferroelectric
polar textures in a cylindrical core-shell nanoparticle. The calculations
reveal a chiral polarization structure containing two oppositely oriented
diffuse axial domains located near the cylinder ends, separated by a region
with a zero-axial polarization. We name this polarization configuration
"flexon" to underline the flexoelectric nature of its axial polarization.
Analytical calculations and numerical simulation results show that the flexon's
chirality can be switched by reversing the sign of the flexoelectric
coefficient. Furthermore, the anisotropy of the flexoelectric coupling is found
to critically influence the polarization texture and domain morphology. The
flexon rounded shape, combined with its distinct chiral properties and the
localization nature near the surface, are reminiscent of Chiral Bobber
structures in magnetism. In the azimuthal plane, the flexon displays the
polarization state of a vortex with an axially polarized core region, i.e., a
meron. The flexoelectric effect, which couples the electric polarization and
elastic strain gradients, plays a determining role in the stabilization of
these chiral states. We discuss similarities between this interaction and the
recently predicted ferroelectric Dyzaloshinskii-Moriya interaction leading to
chiral polarization states.
