Topological superconductivity (TSC) has drawn much attention for its fundamental interest and application in quantum computation. An outstanding challenge is the lack of intrinsic TSC materials with a -wave pairing gap, which has led to the development of an effective -wave theory of coupling -wave gap with Rashba spin-orbit coupling (RSOC). However, the RSOC-strict mechanism and materials pose still both fundamental and practical limitations. Here, we generalize this theory to antisymmetric SOC (ASOC). Using perturbation theory, we demonstrate that 2D crystals, with point groups of , , , , , , , , , , or , can all facilitate the desired ASOC. Remarkably, this enables us to discover 314 TSC candidates by screening 2D material databases, which are further confirmed by first-principles calculations of Majorana boundary modes and the topological invariant of the superconducting gap. Our work fundamentally enriches TSC theory and greatly expands the classes of TSC materials for experimental exploration.
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