We present a general technique for capturing various non-trivial topologies in the band structure of materials, which often arise from spin-orbit coupling. The technique is aimed at insulators and semimetals. Of insulators, Chern, Z2, and crystalline topological insulators can be identified. Of semimetals, the technique captures non-trivial topologies associated with the presence of Weyl and Dirac points in the spectrum. A public software package -- Z2Pack -- based on this technique will be presented. Z2Pack is an easy-to-use, well documented Python package that computes topological invariants and illustrates non-trivial features of Berry curvature. It works as a post-processing tool with all major first-principles codes, as well as with tight-binding models. As such, it can be used to investigate materials with strong spin-orbit coupling.
Dominik Gresch, Alexey A. Soluyanov, Gabriel Autés, Oleg Yazyev, Bogdan A. Bernevig, David H. Vanderbilt, and Matthias Troyer, "Topological classification with Z2Pack
(Conference Presentation)," Proc. SPIE 9931, Spintronics IX, 99313J (Presented at SPIE Nanoscience + Engineering: September 01, 2016; Published: 4 November 2016); https://doi.org/10.1117/12.2239102.5167075280001.
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