First, I will introduce the k.p perturbation theory in solid-state physics. A standard way to construct a k.p invariant Hamiltonian will be discussed in detail. Then, I will briefly talk about the theory of topological quantum chemistry, topological classifications, and symmetry indicators. Finally, an open-source code - CheckTopologicalMat - is released at www.cryst.ehu.es/cryst/checktopologicalmat. I will show you how to use it to check the topology of any material by yourself.

References:

• Barry Bradlyn et al., "Topological quantum chemistry", Nature, 547 (2017).
• Po, H. C. et al., "Symmetry-based indicators of band topology in the 230 space groups", Nat. Comm. 8, 50 (2017).
• Z. Song et al., "Quantitative mappings between symmetry and topology in solids", Nat. Comm. 9, 3530 (2018).
• M. G. Vergniory et al., "A complete catalogue of high-quality topological materials", Nature 566, 480 (2019).