  A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
phase in spin-singlet superconductors. Here we argue that there is a
non-trivial solution for the FFLO vortex phase that exists near the upper
critical field in which the wavefunction has only spatial line nodes that form
intricate and unusual three-dimensional structures. These structures include a
crisscrossing lattice of two sets of non-parallel line nodes. We show that
these solutions arise from the decay of conventional Abrikosov vortices into
pairs of fractional vortices. We propose that neutron scattering studies can
observe these fractional vortex pairs through the observation of a lattice of
1/2 flux quanta vortices. We also consider related phases in
non-centrosymmetric (NC) superconductors.
