Transition temperature and a spatial dependence of the superconducting gap for multilayer high-temperature superconductors

TL;DR

This paper derives formulas for the transition temperature and spatial superconducting gap variation in multilayer high-$T_c$ superconductors, highlighting the role of interlayer hopping in enhancing $T_c$ and applicable to various pairing potentials.

Contribution

It provides a universal theoretical framework for understanding $T_c$ enhancement in multilayered cuprates, emphasizing interlayer hopping as a key factor.

Findings

Interlayer hopping drives high $T_c$ enhancement.

Formulas valid for arbitrary pairing potentials.

Results applicable to Fermi and non-Fermi liquids.

Abstract

We derive the expressions for the transition temperature $(T_{c})$, and the spatial dependence of the superconducting gap for a multilayer high-$T_{c}$ superconductor composed of groups of tightly spaced planes separated by a larger distance. The results are compared with experiment and provide a strong support for an interlayer hopping as the driving force of the large $T_{c}$ enhancement in multilayered compounds. Our results are universal in the sense that they are valid for an arbitrary pairing potential $V_{\bf k k'}$ in the $\rm CuO_{2}$ planes, as well as for both Fermi and nonFermi liquids.