Vortices in layered superconductors with Josephson coupling

Abstract

Strongly anisotropic layered superconductors are considered within the Lawrence-Doniach model. The differential finite-difference sine-Gordon equation is derived for the order-parameter phase differences; boundary conditions are formulated for a vortex lattice. The structure of a tilted vortex is considered. The line energy of a single tilted vortex and the free energy of a tilted vortex lattice in moderate magnetic fields are calculated. Deviations from the three-dimensional London theory are substantial for field orientations close to the layers. As the applied field approaches the ab plane, the orientational lock-in transition (tilted-parallel lattice) occurs provided ${\lambda }_{\mathit{J}}$≲${\lambda }_{\mathit{a}\mathit{b}}$; here ${\lambda }_{\mathit{J}}$=γs is the Josephson length, γ is the anisotropy parameter, and s is the interlayer spacing. If ${\lambda }_{\mathit{J}}$≳${\lambda }_{\mathit{a}\mathit{b}}$, the tilted lattice transforms first into a new type of vortex arrangement that consists of sets of coexisting parallel and perpendicular vortices (combined lattice). Then, as the field further approaches the ab plane, the combined lattice goes over to the parallel one. The angular dependence of the torque is evaluated for tilted, combined, and parallel lattices, which allows one to experimentally distinguish these phases.