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.

对物质拓扑阶段的搜索正在朝着包括磁铁和超导体在内的强相互作用的系统发展，在该系统中，几何，相关性和拓扑之间的量子级相互作用产生了奇特的效应。在过去的十年左右的时间里，扫描隧道显微镜由于其空前的空间分辨率，高精度的电子检测和磁可调性，已经成为探测和发现新兴拓扑物质的强大工具。扫描隧道显微镜可以用来探测各种拓扑现象，以及其他技术的结果的补充。我们讨论了一些适用于探针拓扑的原理验证方法，特别关注在可调谐矢量磁场下进行的研究，这是近期重点研究的一个相对较新的方向。