Universal crossover in surface superconductivity

Chinese Journal of Physics. 2025. Vol. 97. P. 768–776.

Zhu Q., Luo X., Shanenko A., Chen Y.

Interference-induced surface superconductivity (SC), in which the surface critical temperature $T_{cs}$ is enhanced relative to the bulk critical temperature $T_{cb}$, 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 $\tau = (T_{cs} - T_{cb})/T_{cb}$ 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 $\hbar\omega_D$, we reveal a universal crossover in the dependence of $\tau$ on $g$, which is present regardless of a specific value of $\hbar\omega_D$. This crossover is marked by a maximum of $\tau$, indicating that the relative enhancement of the surface critical temperature is greatest within this regime. We also examine the evolution of the ratio $\Delta_{s0}/k_B T_{cs}$ along the crossover, where $\Delta_{s0}$ is the zero-temperature pair potential near the surface (the chain ends), and demonstrate that this ratio can significantly deviate from $\Delta_{b0}/k_B T_{cb}$, where $\Delta_{b0}$ 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.

Keywords: модель Хаббарда, Hubbard model, surface superconductivity, прикраевая сверхпроводимость

Publication based on the results of: Advanced materials and technologies (2025)