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

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.