Theory of anisotropic s-wave superconductivity with point-node like gap minima: analysis of (Y,Lu)Ni_2B_2C

TL;DR

This paper proposes a theoretical mechanism explaining the highly anisotropic s-wave superconductivity with deep point minima in (Y,Lu)Ni$_2$B$_2$C, emphasizing the coexistence of strong electron-phonon coupling and magnetic fluctuations.

Contribution

It introduces a model where magnetic fluctuations induce deep gap minima in s-wave superconductors, aligning with experimental observations in (Y,Lu)Ni$_2$B$_2$C.

Findings

Strong magnetic fluctuations enhance gap anisotropy.

Deep gap minima appear at Fermi surface points connected by nesting vectors.

The model explains experimental gap features in (Y,Lu)Ni$_2$B$_2$C.

Abstract

Recent intensive experimental studies revealed that (Y,Lu)Ni$_2$B$_2$C is an anisotropic s-wave superconductor. In addition, its gap function possesses deep point minima, whose ratio of the gap anisotropy is more than 10. On the theoretical side, however, it is nontrivial to understand the origin of such a peculiar superconductivity. In the present paper, we propose a mechanism of the s-wave superconductivity with deep gap minima, based on the theoretical model where strong electron-phonon coupling as well as the moderate magnetic fluctuations coexist. By analyzing the strong coupling Eliashberg equation, we find that s-wave superconducting gap function owing to the electron-phonon coupling becomes highly anisotropic as the magnetic fluctuations increases. The set of model parameters for realizing the strong gap anisotropy in the present model will be appropriate for (Y,Lu)Ni$_2$B$_2$C. According to the present mechanism, (groups of) pair of gap minima appear at points on the Fermi surface which are connected by the nesting vector ${\bf Q}$, in both cases of s-wave superconductors and non s-wave ones. We briefly discuss other superconductors with highly anisotropic gap function, e.g., PrOs$_{4}$Sb$_{12}$ and Na$_{0.33}$CoO$_2$.