Antiferromagnetism and singlet formation in underdoped high-Tc cuprates: Implications for superconducting pairing

TL;DR

This paper investigates the interplay of antiferromagnetism and singlet formation in underdoped cuprates, revealing that magnetic interactions alone do not induce superconductivity, and discusses implications for pairing mechanisms.

Contribution

It introduces a mean field state with combined antiferromagnetic and flux RVB orders and analyzes its collective modes and pairing interactions, challenging magnetic-only pairing theories.

Findings

Magnetic interactions alone are insufficient for superconductivity in underdoped cuprates.

The effective pairing interaction is pair-breaking for nodeless gaps and negligible for d-wave symmetry.

Superconducting instability requires mechanisms beyond magnetic interactions alone.

Abstract

The extended $t-J$ model is theoretically studied, in the context of hole underdoped cuprates. Based on results obtained by recent numerical studies, we identify the mean field state having both the antiferromagnetic and staggered flux resonating valence bond orders. The random-phase approximation is employed to analyze all the possible collective modes in this mean field state. In the static (Bardeen Cooper Schrieffer) limit justified in the weak coupling regime, we obtain the effective superconducting interaction between the doped holes at the small pockets located around $\bm{k}= (\pm \pi/2, \pm \pi/2)$. In contrast to the spin-bag theory, which takes into acccount only the antiferromagnetic order, this effective force is pair breaking for the pairing without the nodes in each of the small hole pocket, and is canceled out to be very small for the $d_{x^2-y^2}$ pairing with nodes which is realized in the real cuprates. Therefore we conclude that no superconducting instability can occur when only the magnetic mechanism is considered. The relations of our work with other approaches are also discussed.