Spectroscopic Studies of two-dimensional Superconductivity

Abstract Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to the mechanism of high-temperature superconductors and offers an exceptional arena to stabilize 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 meets this need by directly accessing local density of states with lattice-scale resolution. In this review, we summarize recent advances of the study on several representative unconventional superconductors using this technique, focusing on 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 the microscopic insights.