Universal crossover in surface superconductivity

Interference-induced surface superconductivity (SC), in which the surface critical temperature Tcs is enhanced relative to the bulk critical temperature Tcb, has been predicted recently, sparking intensive studies of its properties within an attractive Hubbard model with s-wave pairing. However, a complete understanding of how the relative enhancement τ=(Tcs−Tcb)/Tcb depends on microscopic parameters remains to be developed. In the current work, based on a one-dimensional Hubbard s-wave chain with the BCS energy cutoff and by varying both the pair coupling g and Debye (cutoff) energy ħωD, we reveal a universal crossover in the dependence of τ on g, which is present regardless of a specific value of ħωD. This crossover is marked by a maximum of τ, indicating that the relative enhancement of the surface critical temperature is greatest within this regime. We also examine the evolution of the ratio Δs0/kBTcs along the crossover, where Δs0 is the zero-temperature pair potential near the surface (the chain ends), and demonstrate that this ratio can significantly deviate from Δb0/kBTcb, where Δb0 is the zero-temperature bulk pair potential (deep within the chain). Our findings may offer valuable insights into the search for superconductors with higher critical temperatures.