Topological quantum chemistry*

While the topological materials database has the potential to guide the discovery of new materials, it is important to carefully validate the materials prediction through experimental implementation.

Topological quantum chemistry, while a promising and innovative approach, does come with its set of constraints. This theoretical framework may not be universally applicable, primarily suited for materials with well-defined crystal structures, possibly rendering it less effective in more intricate or disordered systems.

The prevailing emphasis on stoichiometric compounds, characterized by fixed constituent element ratios, imposes a significant limitation. It excludes a substantial array of materials that may exhibit topological behavior but fall short of the stoichiometric criteria. Additionally, the theory predominantly caters to weakly correlated materials, where electron-electron interactions remain relatively small. In strongly correlated systems like certain high-temperature superconductors, both conventional band theory and the topological quantum chemistry approach may prove insufficient in providing comprehensive explanations for their behavior. The basis of the topological quantum chemistry approach in conventional band theory often overlooks electron-electron interactions, which, while reasonable for certain materials, may lead to inaccuracies in predicting the conduct of strongly correlated systems.

Furthermore, the principal focus of topological quantum chemistry lies in electronic band structures, potentially sidelining other critical degrees of freedom like spin or lattice vibrations, which may significantly influence the determination of topological properties. These factors are not entirely accommodated within the existing framework.

Despite these constraints, it's important to acknowledge the substantial contributions of topological quantum chemistry to our comprehension of topological insulators and semimetals. Ongoing research and advancements in the field hold the potential to address some of these challenges and broaden the theory's applicability to a more diverse range of materials and phenomena.

Here we discuss some of the materials that have been successfully realized, but also highlight the limitations of computational predictions and point to new directions for the future.