Surface superconductor-insulator transition induced by electric field

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 with the transport measurements for (Li, Fe)OHFeSe thin flakes [Ma et al., Sci. Bull. 64, 653 (2019); Yin et al., ACS Nano 14, 7513 (2020)].