Ground states and vortex orderings in fields parallel to layers of a layered superconductor

The ground states and the ordering behaviors on cooling in the liquid regime of vortices of a layered superconductor in fields parallel to the layers are theoretically examined using the lowest Landau level approximation for the Lawrence-Doniach model and neglecting randomness. The field-induced change of ground states is largely determined by the magnitude of Abrikosov factor beta(A) and the sign of shear energy in an assumed pinned hexagonal lattice. We find that, in a narrow field range below the stability region of the pinned rhombic solid with no vacant interlayer spacings, a waving structure suggested in a recent numerical simulation is indeed the true ground state, and that a thermal fluctuation correction to the mean field energy is necessary to stabilize other pinned hexagonal solids realizable in lower fields. It is shown by examining the ordering behaviors of vortices in the liquid regime with significant layering effect that the positional correlation in any situation with negligible magnetic screening tends to first develop in the direction parallel to the layers and perpendicular to the field, and concluded that the freezing to a pinned ground state occurs at any field through a single first order transition weakened by the intrinsic pinning effect in nonrandom case.