The role of Berry curvature derivatives in the optical activity of time-invariant crystals

TL;DR

This paper establishes a quantum-geometric framework linking Berry curvature derivatives to optical activity in time-invariant crystals, revealing how symmetry and Berry curvature influence optical phenomena like circular dichroism.

Contribution

It derives the relation between Berry curvature derivatives and optical activity, identifying symmetry constraints and explaining circular dichroism in chiral crystals.

Findings

Circular dichroism arises from non-zero Berry curvature derivatives in chiral crystals.

Symmetry constraints determine which Berry curvature derivatives contribute to optical activity.

The framework enables probing quantum geometry through optical experiments.

Abstract

Quantum geometry and topology are fundamental concepts of modern condensed matter physics, underpinning phenomena ranging from the quantum Hall effect to protected surface states. The Berry curvature, a central element of this framework, is well established for its key role in electronic transport, whereas its impact on the optical properties of crystals remains comparatively unexplored. Here, we derive a relation between optical activity, defined by the gyration tensor, and the k-derivatives of the Berry curvature at optical resonances in the Brillouin zone. We systematically determine which of these derivatives are non-zero or constrained by symmetry across all time-reversal-invariant crystal classes. In particular, we analytically demonstrate that circular dichroism emerges in chiral crystal classes as a result of a non-zero Berry curvature k-derivative along the optical axis, and we interpret this finding based on the conservation of angular momentum in light-matter interactions. This work establishes a quantum-geometric framework for optical activity in solids and it opens new routes to probe quantum geometry via linear and nonlinear optics.