Vortex lattice transformation in d-wave superconductors with Pauli paramagnetic effect

By self-consistently solving the Eilenberger equations in a vortex state, we quantitatively evaluate the free energy for various lattice configurations of the d-wave superconductor under applied magnetic fields along to the c-axis, and discuss the dependence of stable configuration on the paramagnetic effect. By the paramagnetic effect, though the distribution of zero energy local density of states does not extend to the nodal direction above the middle fields, it still has good connection with vortex cores at the nodal directions. Then it makes square vortex lattice stable. We show that there is a first-order orientational transition before rocking into the square vortex lattice at low fields.