Experimental diagnostics of topology
Different topological phases demand different experimental evidence.
$$\text{probe}\in\{\sigma_{xy},\,\gamma,\,\text{edge spectra},\,W(C)\}$$
What this means
Different topological phases demand different experimental evidence.
Deep dive: mathematical and physical mechanism
Integer Hall conductance can measure a Chern invariant in suitable regimes. Angle-resolved photoemission probes surface dispersions; interferometry accesses geometric phases; transport and spectroscopy detect boundary modes. Multiple complementary measurements help exclude trivial alternatives.
How it appears in quantum phenomena
Hall measurements, ARPES, cold-atom band mapping, and scanning tunneling spectroscopy.
Assumptions, caveats and limitations
A single edge peak or a visually striking band crossing is rarely sufficient proof of a topological phase.
Connect the ideas
For context, see the Quantum Phenomena and Applications topic guide and the reading references.