  Recently, a surface superconductor-insulator transition has been predicted
for a bulk superconductor in an electric field applied perpendicular to its
surface. The related calculations were performed within a one-dimensional
Hubbard model by numerically solving the Bogoliubov-de Gennes (BdG) equations
without the Hartree-Fock (HF) interaction potential. The phase diagram of the
surface superconducting, metallic, and insulating states was obtained as
dependent on the electric field and temperature. This diagram was found to be
in agreement with experimental results reported previously for (Li,Fe)OHFeSe
thin flakes. In the present work, by taking into account the HF potential, we
find that the latter acts as a kind of an extra electrostatic potential that
enhances the electric-field effects on the surface states. The qualitative
features of the phase diagram remain the same but the surface
superconductor-insulator transition occurs at significantly lower electric
fields, which supports prospects of its experimental observation in bulk
samples.
