Physical Pictures for Quasisymmetry in Crystals

TL;DR

This paper provides physical interpretations and practical criteria for identifying quasisymmetry in various quantum materials, linking emergent symmetries to material-specific properties through theoretical and computational analysis.

Contribution

It introduces a unified physical framework for understanding quasisymmetry in different materials using density functional theory and group theory, with concrete diagnostic criteria.

Findings

QS corresponds to emergent mirror or inversion symmetries in specific materials

Quantification of QS via a metric $psilon$ measuring subspace invariance

Practical criteria established for diagnosing QS in first-principles calculations

Abstract

Quasisymmetry (QS) provides a novel route to understand and control near-degeneracies, Berry curvature, optical selection rules, and symmetry-protected phenomena in quantum materials. Here we give physical interpretations of the emergence of QS operators across multiple material families. Using density functional theory and the $\mathbf{k}\cdot\mathbf{p}$ formalism, we identify QS subspaces and calculate their representation matrices, quantifying the quasisymmetry via a metric $\epsilon$ that measures subspace invariance. For Sn/SiC and transition-metal dichalcogenide monolayers, QS corresponds to an emergent mirror symmetry, whereas in wurtzite crystals it manifests as an emergent spatial inversion. By contrast, for AgLa the QS appearing in avoided crossings is inherited from a nearby high-symmetry point rather than being an emergent lattice symmetry. Combining group-theoretical analysis and $\mathbf{k}\cdot\mathbf{p}$ modeling, our results establish concrete physical pictures for QS and provide practical criteria to diagnose it in first-principles calculations.