Derivation of the superconducting gap equation for the noncentrosymmetric superconductor Li2Pt3B

TL;DR

This paper derives a microscopic superconducting gap equation for Li2Pt3B, a noncentrosymmetric superconductor with line nodes, predicting an $s_$ wave gap with line nodes as the likely pairing symmetry.

Contribution

It introduces a Hubbard model-based derivation of the gap equation for Li2Pt3B, explaining its nodal behavior and predicting an $s_$ wave pairing symmetry.

Findings

Predicts $s_$ wave gap with line nodes

Explains nodal behavior via microscopic model

Provides a theoretical framework for NCS superconductor Li2Pt3B

Abstract

We present here the mathematical background of our approach, presented in Phys. Rev. B 86, 134526 (2012) regarding the gap function and symmetry for the noncentrosymmetric (NCS) superconductor $Li_2Pt_3B$. As revealed by the experiment, this NCS superconductor gives rise to line nodes in the superconducting order parameter, which is responsible for many of its experimental behaviors. Owing to the enhanced d-character of the relevant bands that cross the Fermi level,the system gets weakly correlated. The nature and symmetry of this nodal behavior is explained from a microscopic viewpoint. In this article starting with an Hubbard model relevant for this NCS system by considering the effect of the onsite Coulomb repulsion on the pairing potential perturbatively, we extract the superconducting gap equation. Further analysis of this equation predicts a $s_\pm$ wave gap function with line nodes as the most promising candidate in the superconducting state.