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We investigate pairing symmetry in the Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) vortex state and vortex lattice, and explain the electronic structure inthese states in terms of pairing symmetry. We show analytically that at theintersection point of FFLO nodal plane and vortex line, only even frequencypairing is present if the Zeeman splitting is negligibly small. With increasingZeeman splitting, odd frequency pairing emerges there. This makes it possibleto interpret the gap structure of the density of states at the intersectionpoint as a manifestation of the even frequency pairing. In the vortex lattice,we find that only odd frequency pairing is present at the core centers, whileat the midpoint of the vortex lines, only even frequency pairing exists. Thus,the odd and even frequency pairings also form the lattice in the vortex latticestate.

Theory of pairing symmetry in Fulde-Ferrell-Larkin-Ovchinnikov vortex state and vortex lattice