Effect of Material-Dependent Boundaries on the Interference Induced Enhancement of the Surface Superconductivity Temperature

Using the tight-binding Bogoliubov–de Gennes formalism, we describe the influence of the surface potential on the superconducting critical temperature at the surface. Surface details are taken into account within the framework of the self-consistent Lang–Kohn effective potential. The regimes of strong and weak coupling of superconducting correlations are considered. Our study reveals that, although the enhancement of the surface critical temperature, originating from the enhancement of the localized correlation due to the constructive interference between quasiparticle bulk orbits, can be sufficiently affected by the surface potential, this influence, nonetheless, strongly depends on the bulk material parameters, such as the effective electron density parameter and Fermi energy, and is likely to be negligible for some materials, in particular for narrow-band metals. Thus, superconducting properties of a surface can be controlled by the surface/interface potential properties, which offer an additional tuning knob for the superconducting state at the surface/interface.