Distorted vortex lattice in a tetrahedral superconductor

The equilibrium shape and the orientation of the vortex lattice are studied for an s-wave tetrahedral superconductor in the vicinity of the upper critical field. The phase diagram, which includes transitions between rhombic and rectangular lattices, is constructed in the parameter space of the Ginzburg-Landau functional. The developed theory is applied to the heavy-fermion superconductor PrOs4Sb12. In a wide range of parameters, the shape of the vortex lattice is only weakly dependent on the temperature. The neutron scattering measurements of the vortex lattice in PrOs4Sb12 can be explained by particularities of the tetrahedral symmetry group and are further supported by analysis of the appropriate band structure calculations.