In recent years, topological quantum materials (TQMs) have attracted intensive attention in the area of condensed matter physics due to their novel topologies and their promising applications in quantum computing, spin electronics and next-generation integrated circuits. Scanning tunneling microscopy/spectroscopy (STM/STS) is regarded as a powerful technique to characterize the local density of states with atomic resolution, which is ideally suited to the measurement of the bulk-boundary correspondence of TQMs. In this review, using STM/STS, we focus on recent research on bismuth-based TQMs, including quantum-spin Hall insulators, 3D weak topological insulators (TIs), high-order TIs, topological Dirac semi-metals and dual TIs. Efficient methods for the modulation of the topological properties of the TQMs are introduced, such as interlayer interaction, thickness variation and local electric field perturbation. Finally, the challenges and prospects for this field of study are discussed.

Carbon, as an indispensable chemical element on Earth, has diverse covalent bonding ability, which enables construction of extensive pivotal carbon-based structures in multiple scientific fields. The extraordinary physicochemical properties presented by pioneering synthetic carbon allotropes, typically including fullerenes, carbon nanotubes, and graphene, have stimulated broad interest in fabrication of carbon-based nanostructures and nanomaterials. Accurate regulation of topology, size, and shape, as well as controllably embedding target spn-hybridized carbons in molecular skeletons, is significant for tailoring their structures and consequent properties and requires atomic precision in their preparation. Scanning probe microscopy (SPM), combined with on-surface synthesis strategy, has demonstrated its capabilities in fabrication of various carbon-based nanostructures and nanomaterials with atomic precision, which has long been elusive for conventional solution-phase synthesis due to realistic obstacles in solubility, isolation, purification, etc. More intriguingly, atom manipulation via an SPM tip allows unique access to local production of highly reactive carbon-based nanostructures. In addition, SPM provides topographic information of carbon-based nanostructures as well as their characteristic electronic structures with unprecedented submolecular resolution in real space. In this review, we overview recent exciting progress in the delicate application of SPM in probing low-dimensional carbon-based nanostructures and nanomaterials, which will open an avenue for the exploration and development of elusive and undiscovered carbon-based nanomaterials.

Scanning probe microscopy (SPM) allows the spatial imaging, measurement, and manipulation of nano and atomic scale surfaces in real space. In the last two decades, numerous advanced and functional SPM methods, particularly atomic force microscopy (AFM), have been developed and applied in various research fields, from mapping sample morphology to measuring physical properties. Herein, we review the recent progress in functional AFM methods and their applications in studies of two-dimensional (2D) materials, particularly their interfacial physical properties on the substrates. This review can inspire more exciting application works using advanced AFM modes in the 2D and functional materials fields.