Two-dimensional superconductivity: a review of computational approaches and emerging phenomena

Two-dimensional (2D) materials offer an exceptional platform for exploring quantum phenomena, as their reduced dimensionality significantly enhances tunability via external parameters. Among these, superconductivity in 2D systems is of particular interest due to its fundamental significance and potential applications in quantum technologies. Despite ongoing experimental challenges in realizing novel 2D superconductors, first-principles calculations have emerged as powerful tools for guiding their prediction and design. While many prior reviews focus broadly on low-dimensional superconductivity, this article specifically surveys computationally predicted 2D superconductors, with an emphasis on the underlying theoretical frameworks and their limitations. We highlight how external perturbations such as strain, doping, chemical functionalization, and intercalation, modify electron-phonon coupling and superconducting critical temperatures, and we examine cases where superconductivity competes or coexists with other quantum orders, including charge density waves and nontrivial band topology. We further discuss the growing role of machine-learning and high-throughput approaches in accelerating materials discovery, along with the challenges associated with data quality and model reliability. Overall, this review underscores the potential and current limitations of first-principles and data-driven approaches in advancing the understanding and discovery of 2D superconductors.