Negative energy antiferromagnetic instantons forming Cooper-pairing "glue" and "hidden order" in high-Tc cuprates

TL;DR

This paper proposes that antiferromagnetic instantons act as a pairing 'glue' in high-Tc cuprates, leading to coexistence of superconductivity and hidden antiferromagnetic order through a novel instantonic mechanism.

Contribution

It introduces a new instantonic framework where magnetic bosons provide pairing glue and coexist with hidden order, supported by self-consistent Eliashberg-like equations.

Findings

Antiferromagnetic instantons can have negative energy due to coupling with Cooper pairs.

Instantonic propagator acts as the Green function for the pairing boson.

Coexistence of superconducting and hidden antiferromagnetic order is possible in cuprates.

Abstract

An emergence of magnetic boson of instantonic nature, that provides a Cooper-'pairing glue', is considered in the repulsive 'nested' Hubbard model of superconducting cuprates. It is demonstrated, that antiferromagnetic instantons of a spin density wave type may have negative energy due to coupling with Cooper pair condensate. A set of Eliashberg-like equations is derived and solved self-consistently, proving the above suggestion. An instantonic propagator plays the role of Green function of pairing 'glue' boson. Simultaneously, the instantons defy condensation of the mean-field SDW order. We had previously demonstrated in analytical form \cite{2,3,4} that periodic chain of instanton-anti-instanton pairs along the axis of Matsubara time has zero scattering cross section for weakly perturbing external probes, like neutrons, etc., thus representing a 'hidden order'. Hence, the two competing orders, superconducting and antiferromagnetic, may coexist (below some Tc) in the form of mean-field superconducting order, coupled to 'hidden' antiferromagnetic one. This new picture is discussed in relation with the mechanism of high temperature superconductivity.