Chern number of thin films of the topological insulator Bi2Se3

In thin films of ${\text{Bi}}_{2}{\text{Se}}_{3}$, the isospin sectors have nontrivial topological properties, which are conventionally characterized by the ${Z}_{2}$ index. The generalized isospin Chern number [E. Prodan, Phys. Rev. B 80, 125327 (2009)] is calculated in the general case where the structural inversion symmetry is broken and the isospin operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\tau}}}_{z}$ is not conserved. The analytical formalism obtained reveals clearly the connection between the isospin Chern number and the ${Z}_{2}$ index. We further demonstrate that the topological characterization based on the isospin Chern number fully agrees with the characteristic spectrum of the edge states in different regimes.