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 and topology. Over the past decade or so, scanning tunnelling microscopy has become a powerful tool to probe and discover emergent topological matter, because of its unprecedented spatial resolution, high-precision electronic detection and magnetic tunability. Scanning tunnelling microscopy can be used to probe various topological phenomena, as well as complement results from other techniques. We discuss some of these proof-of-principle methodologies applied to probe topology, with particular attention to studies performed under a tunable vector magnetic field, which is a relatively new direction of recent focus. We then project the future possibilities for atomic-resolution tunnelling methods in providing new insights into topological matter. The search for topological phases of matter is evolving towards strongly interacting systems, including magnets and superconductors. This Review discusses the proof-of-principle methodologies applied to probe topological magnets and superconductors with scanning tunnelling microscopy. Key points By combining scanning and tunnelling, several proof-of-principle spectro-microscopic methodologies have emerged that are capable of probing the nontrivial topology of electronic and magnetic materials. Explorations of quasi-particle interference and Landau quantization behaviours in materials can be used to elucidate the nature of chiral or helical fermions and their interplay with symmetry-breaking order, such as magnetism, charge order or superconductivity. Bulk-boundary connectivity and its relationship with atomically resolved lattice and magnetic structure probed via topographic measurements are central to understanding emergent topology, such as in kagome lattices. Tunable vector magnetic field capability allows for exploring field-induced novel states in topological matter, including emergent magnetism, superconductivity and strongly correlated phases. In the presence of magnetic field control, spectro-microscopy plays an important role in identifying the nature of localized zero modes or in-gap states, such as the Majorana mode. Scanning tunnelling microscopy-based study on topological materials can be further extended for visualizing Wannier–Bloch duality and can be employed in sub-nanoscale engin