Magnetic Topological Quantum Chemistry

TL;DR

This paper extends the framework of Topological Quantum Chemistry to magnetic crystals by completing the group theory of magnetic space groups, enabling the classification of band topology and surface states in magnetic materials.

Contribution

It derives the corepresentations and compatibility relations for all magnetic space groups, completing a 70-year-old problem and extending topological classification to magnetic crystals.

Findings

Derived symmetry-based indicators of band topology.

Identified bulk and surface states respecting magnetic symmetries.

Made tools and data publicly accessible for magnetic space group analysis.

Abstract

For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.