A microscopic calculation and symmetry argument reveal superconductivity in the vicinity of parity-violating magnetic order. In a crystal structure lacking local space inversion symmetry, an augmented cluster magnetic multipole order may break global inversion symmetry, and therefore it is classified into an odd-parity multipole order. We investigate unconventional superconductivity induced by an odd-parity magnetic multipole fluctuation in a two-dimensional two-sublattice Hubbard model motivated by ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. We find that even-parity superconductivity is more significantly suppressed by spin-orbit coupling than that in a globally noncentrosymmetric system. Consequently, two odd-parity superconducting states are stabilized by magnetic multipole fluctuations in a large spin-orbit coupling region. Both of them are identified as $Z_2$ topological superconducting states. The obtained gap function of intersublattice pairing shows a gapped or nodal structure protected by nonsymmorphic symmetry. Our finding implies a family of odd-parity topological superconductors. Candidate materials are discussed.

• Received 16 July 2018
• Revised 26 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.224510