Novel vortex lattice transition in d-wave superconductors

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We study the vortex state in a magnetic field parallel to the c axis in the framework of the extended Ginzburg Landau equation. We find the vortex acquires a fourfold modulation proportional to (4ϕ) where ϕ is the angle r makes with the a-axis. This term gives rise to an attractive interaction between two vortices when they are aligned parallel to (1,1,0) or (1,-1,0). We predict the first order vortex lattice transition at B=Hcr κ⁻¹ Hc₂(t) from triangular into the square lattice tilted by 45∘ from the a axis. This gives the critical field Hcr a few Tesla for YBCO and Bi2212 monocrystals at low temperatures (T≤ 10 K).