From a leading-order unbiased renormalization group analysis we here showcase the emergence of superconductivity (including the topological ones) from purely repulsive electron-electron interactions in two-dimensional doped Dirac insulators, featuring a Fermi surface. Otherwise a simply connected Fermi surface becomes annular deep inside the topological regime. In the absence of chemical doping, such systems describe quantum anomalous or spin Hall and normal insulators. By considering all symmetry allowed repulsive local four-fermion interactions, we show that the nature of the resulting superconducting states at low temperature follows certain Clifford algebraic selection rules, irrespective of the underlying Fermi surface topology. Within the framework of a microscopic Hubbard model, on-site repulsion among fermions with opposite orbitals (spin projections) typically favors odd-parity topological $p$-wave (conventional even-parity $s$-wave) pairing. Theoretically predicted superconductivity can in principle be observed in experiments once the promising candidate materials for quantum anomalous and spin Hall insulators are doped to foster Fermi surfaces, realizable in quantum materials and on optical lattices of cold atoms.

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• Quantum field theory (low energy)
• Renormalization group
• Topological insulators
• Topological phases of matter
• Topological superconductors
• Superconductors
• Topological materials
• Hubbard model