  In this work we investigate the effects of the short range magnetic
correlations on the gap opening of the topological Kondo insulators. We
consider an additional narrow band to the otherwise completely localized
f-electrons, by adding a term to the periodic Anderson model which allows a
small hopping of the localized electrons between neighboring sites of the
lattice. This new model is adequate to study a novel class of intermetallic 4f
and 5f orbitals materials: the Kondo topological insulators, whose paradigmatic
material is the compound SmB6.
  For simplicity, we consider a version of the periodic Anderson model on a two
dimensional square lattice. The starting point of the model is the 4f-Ce ions
orbitals, with J=5/2 multiplet in the presence of spin-orbit coupling. We
present results of the correlation functions and we show that the short range
antiferromagnetic correlations favors the formation of magnetic moments on the
atoms, and at the same time the existence of these moments opens the
possibility of the spin-flip scattering by the conduction electrons, generating
the Kondo effect, which contribute to the opening of a gap in the density of
states of the system. We also calculate the phase diagram which shows that, as
we vary the Ef level position from the empty regime to the Kondo regime, the
system develops several phases: metallic, band insulator and Kondo topological
insulator. The band structure calculated shows that the model develops a strong
topological insulator.
