Spectroscopic studies of two-dimensional superconductivity

Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to understanding the mechanism of high-temperature superconductors and offers an exceptional arena for stabilizing emergent quantum states enabled by enhanced electron correlations in reduced dimensionality. These states are frequently characterized by spatial modulations and intertwined with competing orders, calling for studies that combine real-space imaging with local spectroscopy. Scanning tunneling microscopy and spectroscopy meet this need by directly accessing the local density of states with lattice-scale resolution. In this review, we summarize recent advances in the study of several representative unconventional superconductors using this technique, focusing on the direct characterization of high-temperature superconducting planes, pair-density waves, and topological superconductivity in both artificial heterostructures and intrinsic materials. We conclude by outlining current challenges and future directions motivated by these microscopic insights.