In this talk I will first review the geometric phase known as Berry phase, and its important role in the band theory of the electronic structure of crystalline materials. I will briefly discuss how the Berry phase, Berry curvature and topological invariants came to be potentially applicable tools to probe topological phases of materials. Next, I would like to give an overview of key topological properties of IV-VI semiconductors and their low dimensional structures such as surfaces, thin films and step defects. In addition, I will present the band topology of (111) planar defect (twin boundary) in SnTe class of material [1].

[1] S. Samadi, R. Rechciński, and R. Buczko, arXiv:2212.14640 (2022)