Symmetry Indicators of Band Topology

Topological invariants of band structures are generally defined using the Bloch wave functions, which make them challenging to compute in realistic first-principles calculations. Spatial symmetries, however, can provide very powerful shortcuts for diagnosing certain classes of topological materials, as is epitomized by the Fu-Kane criterion for inversion-symmetric topological insulators. I will describe our theory of symmetry indicators¹, which utilizes symmetry data in a maximal manner to diagnose band topology in any symmetry setting, including magnetic materials². Aside from serving as an anchor for a more unified theoretical treatment of topological crystalline insulators³, the simplicity of the theory allows us to perform a comprehensive database search and uncovers thousands of topological materials⁴.

[1] Po, H. C., Vishwanath, A. & Watanabe, H. Nat. Commun. 8, 50 (2017).
[2] Watanabe, H., Po, H. C. & Vishwanath, A. Sci. Adv. 4, eaat8685 (2018).
[3] Khalaf, E., Po, H. C., Vishwanath, A. & Watanabe, Phys. Rev. X 8, 031070 (2018).
[4] Tang, F., Po, H. C., Vishwanath, A. & Wan, X. arXiv:1807.09744, 1806.04128, & 1805.07314.