London theory of the crossing vortex lattice in highly anisotropic layered superconductors

A description of Josephson vortices (JV's) crossed by the pancake vortices (PV's) is proposed on the basis of the anisotropic London equations. The field distribution of a JV and its energy have been calculated for both dense (a<<lambda>(j)) and dilute (a>lambda (j)) PV lattices with distance a between PV's and the nonlinear JV core size lambda (j). It is shown that the "shifted" PV lattice (PV's displaced mainly along JV's in the crossing-vortex lattice structure), formed in high out-of-plane magnetic fields B-z>Phi (0)/gamma (2)s(2) [A. E. Koshelev, Phys. Rev. Lett. 83. 187 ( 1999)], transforms into the PV lattice "trapped" by the JV sublattice at a certain field, lower than Phi (0)/gamma (2)s(2), where Phi (0) is the flux quantum. gamma is the anisotropy parameter. and s is the distance between CuO2 planes. With further decreasing B-z, the free energy of the crossing-vortex lattice structure (PV and JV sublattices coexist separately) can exceed the free energy of the tilted lattice (common PV-JV vortex structure) in the case of gammas < <lambda>(ab) with the in-plane penetration depth lambda (ab) if the low (Bx<<gamma>Phi (0)/lambda (2)(ab)) or high (B(x)greater than or similar to Phi (0)/gammas(2)) in-plane magnetic field is applied. It means that the crossing-vortex structure is realized in the intermediate-field orientations, while the tilted vortex lattice can exist if the magnetic field is aligned near the c axis and the ab plane as well. In the intermediate in-plane fields gamma Phi (0)/lambda (2)(ab)less than or similar toB(x)less than or similar to Phi (0)/gammas(2), the crossing-vortex structure with the "trapped" PV sublattice seems to settle in until the lock-in transition occurs since this structure has the lower energy with respect to the tilted vortex structure in the magnetic field H oriented near the ab plane. The recent experimental results concerning the vortex-lattice melting transition and transitions in the vortex-solid phase in Bi2Sr2CaCu2O8+delta single crystals are discussed in the context of the presented theoretical model.