Chiral topological semimetals host quasiparticles that carry a topological invariant — the Chern number — which specifies their handedness. Left-handed and right-handed quasiparticles occupy different nodes in momentum space, and their chirality is protected by the crystal symmetry. The chirality is defined mathematically as the winding number of the Berry phase around the node.
Measuring it directly is another matter.
The chirality is a property of the band structure at a point in momentum space. Angle-resolved photoemission (ARPES) can map band dispersions, but extracting the topological invariant from the dispersion requires tracing the Berry phase around a closed loop — a task that demands phase-sensitive measurements or careful analysis of photoemission matrix elements.
This work develops experimental methods to quantify quasiparticle chirality, making the abstract topological integer into a number read off from data. The measurement exploits the relationship between chirality and the circular dichroism of photoemission: left-handed and right-handed quasiparticles respond differently to left- and right-circularly polarized light. The asymmetry in the photoemission intensity under polarization reversal is a direct probe of the Chern number.
The result converts a classification problem (is this material topological?) into a quantification problem (what is the chirality, and does it match the predicted value?). Classification can tolerate qualitative signatures — the presence or absence of surface states, anomalous transport. Quantification demands agreement between the measured integer and the band-theory prediction. Disagreement would signal either a misidentification of the topological phase or a breakdown of the single-particle description.
The invariant was always there. Now it has a measurement protocol, and measurement turns topology from a label into a test.