Material-specific gap function in the high-temperature superconductors

TL;DR

This paper proposes a theoretical framework based on the t-J model to explain the material-specific gap functions in high-temperature superconductors, supported by experimental evidence showing different pairing symmetries depending on material properties.

Contribution

It introduces a minimal t-J model analysis that accounts for material-dependent gap shapes and pairing symmetries in high-Tc superconductors, linking electronic structure to superconducting properties.

Findings

Materials with large next-nearest-neighbor hopping are nearly pure d-wave.

Nearest-neighbor materials tend to be more s-wave-like.

High hole doping levels favor s-wave pairing.

Abstract

We present theoretical arguments and experimental support for the idea that high-Tc superconductivity can occur with s-wave, d-wave, or mixed-wave pairing in the context of a magnetic mechanism. The size and shape of the gap is different for different materials. The theoretical arguments are based on the t-J model as derived from the Hubbard model so that it necessarily includes three-site terms. We argue that this should be the basic minimal model for high-Tc systems. We analyze this model starting with the dilute limit which can be solved exactly, passing then to the Cooper problem which is numerically tractable, then ending with a mean field approach. It is found that the relative stability of s-wave and d-wave depends on the size and the shape of the Fermi surface. We identify three striking trends. First, materials with large next-nearest-neighbor hopping (such as YBa(2)Cu(3)O(7-x)) are nearly pure d-wave, whereas nearest-neighbor materials (such as La(2-x)Sr(x)CuO(4)) tend to be more s-wave-like. Second, low hole doping materials tend to be pure d-wave, but high hole doping leads to s-wave. Finally, the optimum hole doping level increases as the next-nearest-neighbor hopping increases. We examine the experimental evidence and find support for this idea that gap function in the high-temperature superconductors is material-specific.