  The Spin-Chern ($C_s$) was originally introduced on finite samples by
imposing spin boundary conditions at the edges. This definition lead to
confusing and contradictory statements. On one hand the original paper by Sheng
and collaborators revealed robust properties of $C_s$ against disorder and
certain deformations of the model and, on the other hand, several people
pointed out that $C_s$ can change sign under special deformations that keep the
bulk Hamiltonian gap open. Because of the later findings, the Spin-Chern number
was dismissed as a true bulk topological invariant and now is viewed as
something that describes the edge where the spin boundary conditions are
imposed. In this paper, we define the Spin-Chern number directly in the
thermodynamic limit, without using any boundary conditions. We demonstrate its
quantization in the presence of strong disorder and we argue that $C_s$ is a
true bulk topological invariant whose robustness against disorder and smooth
deformations of the Hamiltonian have important physical consequences. The
properties of the Spin-Chern number remain valid even when the time reversal
invariance is broken.
