Closed Shell States in Periodic Compounds

TL;DR

This paper explores the symmetry properties of closed shell states in periodic compounds, linking atomic shell concepts to band representations and topological stability in layered materials.

Contribution

It introduces a framework connecting atomic shell symmetry to band topology and provides criteria for stability and obstructions in periodic systems.

Findings

Nontrivial determinant representation indicates stable topology.

Shell symmetry concepts extend to band representations.

Obstructive limits identified in line groups.

Abstract

Vanishing of the total angular momentum of the electrons occupying all orbitals of a closed shell in an atom is a textbook fact. Understanding the symmetry content of the atomic shell as irreducible representation of angular momentum, enables straightforward transfer of the notion to (translational or helically) periodic systems. More relevant generalizations naturally appear: stratum shell is intermediate step to physically sound band representations, including elementary and basic ones and connected components. We show that nontrivial determinant representation indicates stable topology of band in single colorless layer groups and obstructive limit in in single colorless line groups.