Theory of Pairing Symmetry in Fulde-Ferrell-Larkin-Ovchinnikov Vortex State and Vortex Lattice

We investigate the pairing symmetry of induced superconductivity in two systems, namely, (i) the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex state and (ii) vortex lattice state without FFLO modulation, and explain the electronic structure in these states in terms of pairing symmetry. We analytically show that, at the intersection point of the FFLO nodal plane and vortex line, only even-frequency pairing is present if the Zeeman splitting is negligible. With increasing Zeeman splitting, odd-frequency pairing emerges at such a point. In the vortex lattice, we find that only odd-frequency pairing is present at core centers, while at the midpoint of vortex lines, only even-frequency pairing exists.