Vortex lattice structures in Rashba noncentrosymmetric superconductors in magnetic fields parallel to the basal plane ͑H Ќ c͒ are examined based on the BCS-like Hamiltonian and the resulting Ginzburg-Landau functional. Due to the momentum-dependent anisotropy of the Zeeman effect induced by the broken inversion symmetry, the vortex lattice in higher fields generally shows some unidirectional modulation of Fulde-FerrellLarkin-Ovchinnikov type orienting in the plane perpendicular to H. However, the direction of the modulation and the lattice structure depend significantly on the underlying pairing symmetry: when the mixing between spin singlet and triplet pairing components is negligible, the resulting modulated structure tends to have reflection symmetry, while the vortex lattice in systems with a significant singlet-triplet mixing has no reflection symmetry in most cases. The latter result implying the presence in real materials of two degenerate orientations of the lattice structure separated by domain walls may be relevant to the extremely low-magnetic decay rate observed in CePt 3 Si.

To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several higher LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the melting transition in higher fields is significantly weakened with decreasing the field. Nevertheless, a genuine crossover to the consecutive continuous melting picture intervened by a hexatic liquid is not found within the use of the GL model. PACS numbers:

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