Universal Relation Connecting Fermi Surface to Symmetry of the Gap Function in BCS-Like Superconductors

TL;DR

This paper derives a universal relation linking the Fermi surface shape to the symmetry of the superconducting gap in BCS-like superconductors, highlighting the influence of next-nearest neighbor interactions and implications for cuprates.

Contribution

It introduces a universal relation connecting Fermi surface geometry to gap symmetry, considering next-nearest neighbor effects, and discusses its application to cuprate superconductors.

Findings

Fermi surface shape can be deduced from gap symmetry.

Next-nearest neighbor interactions influence Fermi surface and Luttinger's theorem.

Universal relation applies to BCS-like superconductors.

Abstract

A universal relation connecting Fermi surface (FS) to the symmetry of the gap function in BCS-like superconductors is derived. It is found that the shape of the FS can be deduced directly from the symmetry of the superconducting gap function, and is also influenced by the next nearest-neighbor overlapping. The application of this relation to cuprate superconductors is discussed. There is observed an interesting property that Luttinger's theorem perfectly holds for the tight-binding band while it is violated by inclusion of the next nearest-neighbor overlapping integral.