Table 1: Symmetry-breaking orders can be probed/defined through linear responses. But topological order cannot be probed/defined through linear responses. We need topological probes to define topological orders.

OrderExperiment

Crystal orderX-ray diffraction
Ferromagnetic orderMagnetization
Antiferromagnetic orderNeutron scattering
Superuid orderZero viscosity and vorticity quantization
Topological orderTopological degeneracy
(Global dancing pattern)non-Abelian geometric phase