# Topological quantum chemistry

## TL;DR

Topological Quantum Chemistry introduces a comprehensive band theory linking topology with chemical bonding, enabling classification and prediction of topological insulators across all crystal symmetries, addressing the scarcity of known TIs.

## Contribution

It presents a complete electronic band theory that unifies topology and local chemical bonding, classifies all possible band structures, and predicts new topological insulators.

## Key findings

- Classified all band structures for 230 crystal symmetries.
- Identified which structures are topologically nontrivial.
- Predicted numerous new topological insulators.

## Abstract

The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material databases, only several hundred of them are topologically nontrivial. Are TIs that esoteric, or does this reflect a fundamental problem with the current piecemeal approach to finding them? To address this, we propose a new and complete electronic band theory that highlights the link between topology and local chemical bonding, and combines this with the conventional band theory of electrons. Topological Quantum Chemistry is a description of the universal global properties of all possible band structures and materials, comprised of a graph theoretical description of momentum space and a dual group theoretical description in real space. We classify the possible band structures for all 230 crystal symmetry groups that arise from local atomic orbitals, and show which are topologically nontrivial. We show how our topological band theory sheds new light on known TIs, and demonstrate the power of our method to predict a plethora of new TIs.