Band Representations and Topological Quantum Chemistry

Understand

In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators.

• We begin with an overview of the properties of crystal symmetry groups in position and momentum space.
• Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures.
• By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be catalogued and classified.