Competing superconducting, magnetic and charge orderings in the AF Heisenberg-Kondo lattice with Dirac electrons

TL;DR

This paper models a complex lattice system with Dirac electrons, revealing how competing superconducting, magnetic, and charge orderings emerge from fundamental interactions, providing insights into high-temperature superconductivity.

Contribution

It introduces a unified theoretical framework showing how multiple competing orders arise from the antiferromagnetic Heisenberg-Kondo lattice with Dirac electrons.

Findings

Derives an effective interaction among itinerant electrons including superconducting, magnetic, and charge gap terms.

Shows that these competing interactions originate from the original Kondo magnetic interaction.

Provides a basis for understanding complex phase diagrams in correlated electron materials.

Abstract

Many recently discovered advanced materials, such as high-Tc cuprates, iron pnictides and several heavy-fermions, exhibit a rich phase diagram suggesting the presence of different competing interactions that would lead to various types of ordering. Nevertheless, there is not yet a clear unifying picture allowing the understanding of the detailed mechanisms that generate such competing interactions. Having such a picture, however, could quite well be at the very roots of the requirements for understanding high-Tc superconductivity in cuprates and pnictides, for instance. In this work we consider the antiferromagnetic (AF) Heisenberg-Kondo lattice, consisting of localized spins with AF exchange interactions between nearest neighbors on a square lattice and itinerant electrons, which undergo a magnetic Kondo interaction with the localized spins, but are otherwise non-interacting. Using the Schwinger-boson (CP$^1$) formalism and assuming the electrons are Dirac-like, we integrate on the localized degrees of freedom thereby obtaining the effective interaction among the itinerant electrons. This contains a BCS-like superconducting term, a Nambu-Jona-Lasinio-like, charge gap term and a Ising and Heisenberg-like magnetic terms. All these four competing interactions, therefore are generated by the original Kondo magnetic interaction.