Superconducting 3D-sample with general boundary conditions in a tilted magnetic field

We consider a mesoscopic superconducting three-dimensional cube immersed in a tilted magnetic field H oriented along an angle θ with respect to the z-axis, in the xz plane. The sample is in contact with a metallic material or with another superconductor in the xz and yz planes, while the z=0 plane remains in contact with a dielectric material. These boundary conditions are simulated by the de Gennes extrapolation length b. We analyzed the magnetic induction, the superconducting electron density, and the magnetization curves as functions of H for different values of b on the lateral surfaces of the sample. We show that the magnetization and the vortex configuration depend on θ and b. An analytical linear and exponential dependence of the maximum of the magnetization on θ and b, respectively, was found.