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

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