Weak coupling model for s*- and d-wave superconductivity

TL;DR

This paper investigates the phase diagram of the $t-J$ model, revealing that $d$-wave superconductivity is dominant near half-filling, with maximum $T_c$ around 0.7 electrons per site, and that extended $s$-wave pairing occurs only at low doping.

Contribution

It provides a detailed analysis of the superconducting phases in the $t-J$ and $t-t'-J$ models, highlighting the conditions favoring $d$-wave pairing and the relationship between $T_c$ and magnetic ordering.

Findings

$d$-wave pairing dominates near half-filling.

Maximum $T_c$ occurs at about 0.7 electrons per site.

Extended $s$-wave pairing occurs only at low doping.

Abstract

The phase diagram of the unconstrained $t-J$ model is calculated using the random phase approximation. It is found that the extended $s$ and the $d_{x^2-y^2}$-channels are {\em not} degenerate near half filling. Extended $s$-pairing with a low $T_c$ occurs only for a band containing less then 0.4 electrons or holes per unit cell, whereas in a large region around half-filling $d$-wave pairing is the only stable superconducting solution. At half filling superconductivity is suppressed due to the formation of the anti-ferromagnetic Mott-Hubbard insulating state. By extending the analysis to the unconstrained $t-t'-J$ model, it is proven that, if a Fermi surface is assumed similar to the one that is known to exist in cuprous oxide superconductors, the highest superconducting $T_c$ is reached for about $0.7$ electron per site, whereas the anti-ferromagnetic solution still occurs for $1$ electron per site. It is shown, that the maximum $d$-wave superconducting mean field transition temperature is half the maximum value that the Ne\`el temperature can have in the Mott-insulating state.