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In this work we investigate the effects of the short range magneticcorrelations on the gap opening of the topological Kondo insulators. Weconsider an additional narrow band to the otherwise completely localizedf-electrons, by adding a term to the periodic Anderson model which allows asmall hopping of the localized electrons between neighboring sites of thelattice. This new model is adequate to study a novel class of intermetallic 4fand 5f orbitals materials: the Kondo topological insulators, whose paradigmaticmaterial is the compound SmB6.  For simplicity, we consider a version of the periodic Anderson model on a twodimensional square lattice. The starting point of the model is the 4f-Ce ionsorbitals, with J=5/2 multiplet in the presence of spin-orbit coupling. Wepresent results of the correlation functions and we show that the short rangeantiferromagnetic correlations favors the formation of magnetic moments on theatoms, and at the same time the existence of these moments opens thepossibility of the spin-flip scattering by the conduction electrons, generatingthe Kondo effect, which contribute to the opening of a gap in the density ofstates of the system. We also calculate the phase diagram which shows that, aswe vary the Ef level position from the empty regime to the Kondo regime, thesystem develops several phases: metallic, band insulator and Kondo topologicalinsulator. The band structure calculated shows that the model develops a strongtopological insulator.

The role of the short range magnetic correlations on the gap opening of the topological Kondo insulators