Calculating Topological Invariants with Z2Pack

The topological phase of non-interacting electronic bandstructure can be classified by calculating integer invariants. In this chapter, we introduce the Chern invariant that classifies 2D materials in the absence of symmetry. We then show that this invariant can be used as the building block for the classification of topological insulators, semimetals, and symmetry-protected topological phases. We show how this classification is performed in practice by introducing Z2Pack, a tool which allows calculating topological invariants from k⋅p and tight-binding models, as well as first-principles calculations