In this work, fifirstly, we study two one dimensional physics models, one for an insulating material
such as polyacetylene called SSH model and the other of a p-wave superconductor called
Kitaev. We also study the fundamental states of an alternative model from the previous two,
that is, a physical model that contains an insulating part and a superconducting part. The hybrid
superconducting model that we study for limit conditions such as µ is equal to zero and ∆ is equal
to zero, becomes the SSH model as expected.The energy spectra obtained for this unconventional
model show the similarity it has with the two conventional models mentioned, that is, it presents
the existence of an energy gap, which closes or opens as we vary "k"and others parameters
(e.g. superconducting correlations, chemical potential and hopping). Also, we fifind non-trivial
topological phases in certain limits of the hybrid model. We characterized the topological phase
transitions through the gao closing and a topological invariant called winding number. Through
the winding number, we can differentiate the topological phases or topological regions thaat we
fifind for different values of hopping and superconducting correlations parameters.
One way to be able to differentiate the phases for both the SSH and Kitaev models, is through
the winding number, which we also use for the hybrid model. Through the winding number we
can differentiate the phases or topological regions that we fifind for different values of the hopping
parameters. We also fifind the symmetries of the two conventional models and the alternative
model, which by their established form the three models have three discrete symmetries, Chiral,
Reversal Time and Particle-hole. With these symmetries we fifind the topological class to which
they belong.