  Topological phases are a fertile playground emerging from within
ferroelectric superlattices. Herein, using phase-field simulations, we
demonstrate the local control of the skyrmion phase with applied electric
field. Under a small electric field, the skyrmions inside the electrode can be
erased and recovered reversibly. While a topological transition to labyrinth
domains requires a high field, which can switch back to skyrmions with a
relatively small electric field. It is shown that the shrinking and dissipation
of the skyrmions leads to a large reduction in the dielectric permittivity with
the magnitude of reduction depends on the electrode size.
