Stimulated by recent studies of superconductivity and magnetism with local and global broken inversion symmetry, we investigate the superconductivity in magnetic multipole states in locally noncentrosymmetric metals. We consider a one-dimensional zigzag chain with sublattice-dependent antisymmetric spin-orbit coupling and suppose three magnetic multipole orders: monopole order, dipole order, and quadrupole order. It is demonstrated that the Bardeen-Cooper-Schrieffer state, the pair-density wave (PDW) state, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are stabilized by these multipole orders, respectively. We show that the PDW state is a topological superconducting state specified by the nontrivial ${\mathbb{Z}}_2$ number and winding number. The origin of the FFLO state without macroscopic magnetic moment is attributed to the asymmetric band structure induced by the magnetic quadrupole order and spin-orbit coupling.

• Received 30 March 2016
• Revised 21 May 2016

DOI:https://doi.org/10.1103/PhysRevB.93.224507