Spatial Line Nodes and Fractional Vortex Pairs in the Fulde-Ferrell-Larkin-Ovchinnikov Vortex State of Spin-Singlet Superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel 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 noncentrosymmetric superconductors.

Figure 1

Helical spatial line nodes in the gap for the multiple-$q$ phase of NC superconductors. The centers of the helices form a 2D hexagonal lattice perpendicular to the field.

Figure 2

Crisscrossing lattice of nodal lines in the FFLO vortex phase with $\mathit{\tau }=(a,b)/2$. The ● in the top figure shows the nodes perpendicular to the applied magnetic field for $z=0$. As $z$ is changed slightly, these nodes move as illustrated by the arrows in the upper right of this figure. The lower figure shows a cross section as seen from the $y$ direction. The different colored lines correspond to the nodal lines with different $y$ positions.