Resolving exotic quantum states using scanning tunneling microscopy

Scanning tunneling microscopy (STM) is a pivotal surface-imaging technique that reveals intricate atomic and electronic structures. Its remarkable subatomic spatial resolution, coupled with the energy-resolved local density of states, provides insights into both the local electronic properties and global band structures. Recent advancements in STM, including a breakthrough in charge-density manipulation, have broadened the scope of its research. This review delves into the experimental methodologies for probing the electronic structures of various topological materials, including topological insulators, semimetals, and superconductors. It explores techniques such as Landau-level spectroscopy and quasi-particle interference measurements. Additionally, it examines the influence of topological phase transitions and electron correlations that can be modulated by in situ electrical fields in two-dimensional samples.