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

Abstract

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<λJ) and dilute (a>λJ) PV lattices with distance a between PV’s and the nonlinear JV core size λJ. 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 Bz>Φ0/γ2s2 [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 Φ0/γ2s2, where Φ0 is the flux quantum, γ is the anisotropy parameter, and s is the distance between CuO2 planes. With further decreasing Bz, 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 γs<λab with the in-plane penetration depth λab if the low (Bx<γΦ0/λab2) or high (Bx≳Φ0/γs2) 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 γΦ0/λab2≲Bx≲Φ0/γs2, 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+δ single crystals are discussed in the context of the presented theoretical model.

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