Probing topological quantum matter with scanning tunnelling microscopy

The search for topological phases of matter is evolving towards strongly interacting systems, including magnets and superconductors, where exotic effects emerge from the quantum-level interplay between geometry, correlation topology. Over past decade or so, scanning tunnelling microscopy has become a powerful tool to probe discover emergent matter, because its unprecedented spatial resolution, high-precision electronic detection magnetic tunability. Scanning can be used various phenomena, as well complement results other techniques. We discuss some these proof-of-principle methodologies applied topology, with particular attention studies performed under tunable vector field, which relatively new direction recent focus. then project future possibilities atomic-resolution methods in providing insights into matter.