Dislocations and vortices in pair-density-wave superconductors

With the groundbreaking work of Fulde, Ferrell, Larkin and Ovchinnikov, it was realized that superconducting order can also break translational invariance, leading to a phase in which the Cooper pairs develop a coherent periodic spatially oscillating structure. Such pair-density-wave (PDW) superconductivity has become relevant in a diverse range of systems, including cuprates, organic superconductors, heavy-fermion superconductors, cold atoms and high-density quark matter. Here we show that, in addition to charge-density-wave (CDW) order, there are PDW ground states that induce spin-density-wave (SDW) order when there is no applied magnetic field. Furthermore, we show that PDW phases support topological defects that combine dislocations in the induced CDW/SDW order with a fractional vortex in the usual superconducting order. These defects provide a mechanism for fluctuation-driven non-superconducting CDW/SDW phases and conventional vortices with CDW/SDW order in the core.