The Quantized Chirality

Chiral topological invariants characterize band structures that break mirror or inversion symmetries in ways that produce handedness — a preference for left or right that is encoded in the topology of the Bloch wavefunctions. These invariants (Dixmier-Douady classes, Hopf indices) have been defined mathematically but never measured experimentally, because they couple to observables that have not been identified.

Jankowski, Palumbo, and Slager (arXiv:2603.28752, March 2026) show that chiral topological invariants produce integer-quantized differences in dichroic excitation rates — a new quantized observable accessible to optical experiments. When a material with chiral band topology is illuminated with light of opposite handedness (left-circular vs. right-circular), the excitation rates differ by an integer determined by the topological invariant. The quantization is exact, not approximate — it is protected by the same topology that defines the invariant.

The coupling is through higher-tensor Berry curvatures — generalizations of the standard Berry curvature that involve derivatives with respect to multiple crystal momentum components simultaneously. These higher-tensor quantities have been theoretically defined for years but have had no known experimental signature. The optical dichroism couples to them because the light-matter interaction at higher multipole orders (beyond the electric dipole approximation) probes exactly these higher-tensor structures.

Superchiral light — light with enhanced local optical chirality, achievable in current experimental setups using crossed beams or plasmonic nanostructures — provides the probe. Standard circularly polarized light couples to the lowest-order chirality; superchiral light enhances the coupling to higher-tensor Berry curvatures, making the quantized dichroism observable above the experimental noise floor.

The structural observation: a class of topological invariants thought to be experimentally inaccessible becomes measurable through a specific optical response. The connection was hidden because the standard electric dipole coupling does not see the higher-tensor Berry curvatures — it takes the next order in the multipole expansion, probed by superchiral light, to couple to the invariant. The measurement existed all along; it just required the right light.