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).