High-Throughput Discovery of Noncentrosymmetric Topological Materials Beyond Symmetry-Based Indicators

The prediction and discovery of 3D topological insulators (TIs) and semimetals (TSMs) has been dramatically accelerated via the methods of symmetry-based indicators (SIs) and Topological Quantum Chemistry, which have facilitated the identification of thousands of TI and TSM materials. These efforts revealed that over half of known nonmagnetic 3D materials exhibit topological features at the Fermi level. However, this is only a lower bound on the actual number of topological materials, since SIs cannot distinguish trivial from topological states in over half of the nonmagnetic symmetry groups (SGs). This issue is particularly acute in noncentrosymmetric (e.g. polar, chiral) SGs, in which TIs and TSMs are expected to exhibit a richer range of responses than in centrosymmetric materials, but are largely undetectable by SIs. We introduce a novel group-theory-based, numerically efficient method for detecting TIs and TSMs that exceeds the mathematical bounds of SIs by leveraging information encoded in the electronic spin degree of freedom. We apply our method to the fully ab-initio high-throughput discovery of noncentrosymmetric TIs and TSMs, and detail material candidates overlooked by all previous analytic screening schemes.