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Vortex lattice states occurring in noncentrosymmetric superconductors withthe spin-orbit coupling of Rashba type under a magnetic field parallel to thesymmetry plane are examined by assuming the $s$-wave pairing case and in anapproach combining the quasiclassical theory with the Landau level expansion ofthe superconducting order parameter. The resulting field-temperature phasediagrams include not only a discontinuous transition but a continuous crossoverbetween different vortex lattice structures, and, further, a critical end pointof a structural transition line is found in an intermediate field and at a lowtemperature in the present approach. It is pointed out that the strange fielddependence of the vortex lattice structure is a consequence of that of ananisotropy stemming from the Rashba spin-orbit coupling, and that the criticalend point is related to the helical phase modulation peculiar to thesematerials in the ideal Pauli-limited case. Further, calculation results on thelocal density of states detectable in STM experiments are also presented.

Quasiclassical analysis of vortex lattice states in Rashba noncentrosymmetric superconductors