  It is well-known that the electric field can induce phase transitions between
superconducting, metallic and insulating states in thin-film materials due to
its control of the charge carrier density. Since a similar effect on the charge
carriers can also be expected for surfaces of bulk samples, here we investigate
the transformation of the surface states in a superconductor under an applied
screened electric field. Our study is performed by numerically solving the
self-consistent Bogoliubov-de Gennes equations for the one-dimensional
attractive Hubbard model. It is found that the surface insulating regime occurs
at sufficiently large (but still experimentally accessible) electric fields.
Our calculations yield the phase diagram of the surface superconducting,
metallic, and insulating states for a wide range of temperatures and applied
fields. Our results are in qualitative agreement with the phase diagram
obtained by the transport measurements for (Li, Fe)OHFeSe thin flakes [Sci.
Bull. 64, 653 (2019); ACS Nano 14, 7513 (2020)].
