  We study a model of two dimensional, topological superconductivity on a
square lattice. The model contains hopping, spin orbit coupling and a time
reversal symmetry breaking Zeeman term. This term, together with the chemical
potential act as knobs that induce transitions between trivial and topological
superconductivity. As previously found numerically, the transitions are seen in
the entanglement entropy as cusps as a function of model parameters. In this
work we study the entanglement entropy analytically by keeping only its most
important components. Our study is based on the intuition that the number of
Fermi surfaces in the system controls the topological invariant. With our
approximate expression for the entanglement entropy we are able to extract the
divergent entanglement entropy derivative close to the phase transition.
