The presence of topological defects in apolar chiral liquid crystals cause
orientational distortions, leading to non-uniform strain. This non-uniform
strain generates an electric polarization response due to the flexoelectric
effect, which induces an internal electric field. Associated to this electric
field is an electrostatic self-energy, which has a back-reaction on the
director field. Calculation of this internal electric field and its resulting
back-reaction on the director field is complicated. We propose a method to do
such, adapting a method recently developed to study the magnetostatic
self-interaction effect on skyrmions in chiral ferromagnets. Bloch skyrmions in
chiral magnets are solenoidal and are unaffected by the magnetostatic
self-interaction. Cependant, Bloch skyrmions in liquid crystals yield
non-solenoidal flexoelectric polarization and, thus, are affected by the
electrostatic self-interaction. Additionally, as the flexoelectric coefficients
are increased in strength, a transition from a hopfion to a skyrmion is
observed in three-dimensional confined systems.

Cet article explore les excursions dans le temps et leurs implications.

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