Two-dimensional superconductors with intrinsic p-wave pairing or nontrivial band topology

Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC), enabled by real-space superconducting proximity effect, reciprocal-space superconducting proximity effect, and intrinsic TSC. Whereas the first scheme has so far been most extensively explored, the subtle difference between the other two remains to be fully substantiated. We then move on to candidate intrinsic or p-wave superconductors, including Sr2RuO4,UTe2,Pb3Bi, and graphene-based systems. For TSC systems that rely on proximity effects, the emphases are mainly on the coexistence of superconductivity and nontrivial band topology, as exemplified by transition metal dichalcogenides, cobalt pnictides, and stanene, all in monolayer or few-layer regime. The review completes with discussions on the three dominant tuning schemes of strain, gating, and ferroelectricity in acquiring one or both essential ingredients of the TSC, and optimizations of such tuning capabilities may prove to be decisive in our drive towards braiding of Majorana zero modes and demonstration of topological qubits.