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Regarding three-dimensional (3D) topological insulators and semimetals as astack of constituent 2D topological (or sometimes non-topological) layers is auseful viewpoint. Primarily, concrete theoretical models of the paradigmatic 3Dtopological phases such as Weyl semimetal (WSM), strong and weak topologicalinsulators (STI/WTI), and Chern insulator (CI), are often constructed in thatway. Secondarily, fabrication of the corresponding 3D topological material isalso done in the same spirit; epitaxial growth technique is employed, makingthe resulting sample in the form of a thin film. Here, in this paper wecalculate $\mathbb{Z}$- and $\mathbb{Z}_2$-indices and study evolution of thetopological properties of such thin films of 3D topological systems, makingalso a comparative study of CI- vs. TI-type models belonging to differentsymmetry classes in this respect. Through this comparative study we suggestthat WSM is to CI as STI is to WTI. Finally, to test the robustness of ourscenario against disorder and relevance to experiments we have also studiednumerically the two-terminal conductance of the system using transfer matrixmethod.

Comparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view