Predicting and Understanding Quantum Spin Hall Insulators with the Help of Compressed Sensing/SISSO.

Quantum Spin Hall insulators (QSHIs), i.e., two-dimensional insulators with conducting edge states protected by time-reversal symmetry, have attracted considerable scientific interest in recent years. In this work, we perform first-principles calculations to compute the Z₂-invariant for 220 functionalized honeycomb-lattice materials. Using the recently developed sure independence screening and sparsifying operator (SISSO) method [1], we derive a "map of materials", in which metals, trivial insulators, and QSHIs are spatially separated. The axes of this map are defined by physically meaningful descriptors, i.e., non-linear functions that only depend on the properties of the material’s constituent free atoms. First, this yields fundamental insights into the mechanisms driving topological transitions. Second, we are able to predict the topological character of materials that are not part of the originally investigated set just from their position on the map (predictive power greater than 95%). By this means, we are able to predict 89 yet unknown QSHIs.
[1] Runhai Ouyang, et al., arXiv:1710.03319 (2017).