Vortex lattice transition in d-wave superconductors

Making use of the extended Ginzburg-Landau theory, which includes the fourt h-order derivative term, we study the vortex stare in a magnetic held paral lel to the c axis. The vortex core structure is distorted due to the higher -order term, which reveals the fourfold symmetry. Further, this distortion gives rise to the core interaction energy which favors a square lattice til ted by 45 degrees from the a axis, The triangular vortex lattice in small f ield region transforms into the rhombic vortex lattice (i.e., the square vo rtex lattice tilted 45 degrees from the (a axis) at B = H-cr similar to kap pa (-1) H-c2(t), where kappa is the Ginzburg-Landau parameter and H-c2(t) i s the upper critical field. Therefore, in most of the B-T phase diagram the vortex lattice is rhombic. The transition is of the second order and the a ssociated jump in the specific heat should be accessible experimentally.