Symmetry classes of triplet vortex lattice solutions of the Bogoliubov de-Gennes equation in a square lattice

We give a group theoretical classification of the triplet vortex lattice states of the two-dimensional Hubbard model with a nearest neighbor ferromagnetic exchange interaction in a uniform magnetic field. We obtain 11 types of tetragonal vortex lattice states for the magnetic flux phi=phi0/p2 (phi0=ch/2e is the flux quantum, p is an integer) through a unit cell of crystal lattice. We show the configurations of the order parameters corresponding to axial phase, up spin phase, planar phase and bipolar phase. It is clarified what types of vortex lattice phase are possible in triplet superconductors such as Sr2RuO4 with basal square lattice when the symmetry of magnetic translation is considered