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Vortex lattice structures in Rashba noncentrosymmetric superconductors inmagnetic fields parallel to the basal plane (${\bf H} \perp c$) are examinedbased on the BCS-like Hamiltonian and the resulting Ginzburg-Landau functional.Due to the momentum dependent anisotropy of the Zeeman effect induced by thebroken inversion symmetry, the vortex lattice in higher fields generally showssome unidirectional modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) typeorienting in the plane perpendicular to ${\bf H}$. However, the direction ofthe modulation and the lattice structure depend significantly on the underlyingpairing symmetry: When the mixing between spin singlet and triplet pairingcomponents is negligible, the resulting modulated structure tends to havereflection symmetry, while the vortex lattice in systems with a significantsinglet-triplet mixing has no reflection symmetry in most cases. The latterresult implying the presence in {\it real} materials of two degenerateorientations of the lattice structure separated by domain walls may be relevantto the extremely low magnetic decay rate observed in CePt$_3$Si.

Vortex lattice structure dependent on pairing symmetry in Rashba superconductors