Microscopic description of surface superconductivity
In this work, we revisit the problem of superconductivity under the influence of boundary effects. By solving the Bogoliubov-de Gennes (BdG) equations for the tight-binding model, we demonstrate that the critical temperature of the nucleation of superconductivity near a sample surface can be considerably enhanced as compared to its bulk value. To bring to light this effect, we investigate different methods to solve numerically the BdG equations, including the continuous and Anderson approximations, and perform the calculations for a wide range of the system parameters. We obtain that all the self-consistent BdG eigenstates are delocalized and occupy the entire volume of the sample. Our results reveal that the enhancement of the surface critical temperature originates from the quantum interference of different BdG states contributing to the order parameter. We also find that the surface enhancement is the largest when the conduction band is symmetric with respect to the Fermi level, particularly, the half filling is an important proviso for the pronounced surface effect on the critical temperature. The approximate continuous model as well as the Anderson approximation do not capture the main feature of the surface effect. In addition, our study of this effect versus surface roughness reveals its fragile character.