Superconducting properties of a parallelepiped mesoscopic superconductor: A comparative study between the 2D and 3D Ginzburg–Landau models

• Effect of a pillar on the thermodynamical properties of a 2- and 3-dimensional superconducting parallelepiped is studied.
• Magnetic properties depend on the choice among the 2D and 3D approaches of the Ginzburg–Landau equations.
• An analytical dependence of the thermodynamic fields and the magnetization as functions of the lateral dimension is found.
• A 3D superconductor can present a large and rich variety of vortex configurations.

We theoretically investigate the local magnetic field, order parameter and supercurrent profiles of a parallelepiped mesoscopic superconductor submersed in an applied magnetic field; this same geometry with a pillar on its top surface is also considered. Our investigation was carried out by solving the three-dimensional time-dependent Ginzburg–Landau (TDGL) equations. We obtain the magnetization curve as a function of the external applied magnetic field for several sample sizes. We have determined an analytical dependence of the thermodynamic fields and the magnetization as functions of the lateral dimension of the superconductor. Finally, a systematic comparative study of the two- and three-dimensional approaches of the Ginzburg–Landau model is carried out.