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arXiv · 2107.03222

The topological invariants of rotationally symmetric crystals

Jans Henke·Mert Kurttutan·Jorrit Kruthoff·Jasper van Wezel
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Abstract

Recent formal classifications of crystalline topological insulators predict that the combination of time-reversal and rotational symmetry gives rise to topological invariants beyond the ones known for other lattice symmetries. Although the classification proves their existence, it does not indicate a way of calculating the values of those invariants. Here, we show that a specific set of concentric Wilson loops and line invariants yields the values of all topological invariants in two-dimensional systems with pure rotation symmetry in class AII. Examples of this analysis are given for specific models with two-fold and three-fold rotational symmetry. We find new invariants that relate to the presence of higher-order topology and corner charges.

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Jans Henke, Mert Kurttutan, Jorrit Kruthoff, Jasper van Wezel. 2021-07-07. The topological invariants of rotationally symmetric crystals. https://doi.org/10.1103/physrevb.104.l201110

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