Magnetic flux penetration into the high-temperature superconductors

The fundamentals governing the penetration of magnetic flux into the high-temperature superconductors are discussed. The anisotropic Ginzburg-Landau theory is used to describe the anisotropic critical fields and magnetization in these materials. To take into account the layered nature of the high-temperature superconductors on an atomic length scale, the Lawrence-Doniach theory is introduced, and the representation of a vortex line as a stack of 2D pancake vortices connected by Josephson strings is explained. The consequences for flux pinning and the critical-current density are reviewed. The penetration of magnetic flux into strips and disks of type-II superconductors also is discussed. First, the magnetic field and current-density profiles of strips and disks are considered for the conditions that (a) the critical current is dominated by bulk pinning and (b) the distinction between B and H can be ignored. Next, the corresponding profiles are described for the case that (a) bulk pinning is negligibly small, (b) the distinction between B and H is accounted for, and (c) there is a pronounced geometrical barrier. Finally, the behavior is discussed for the case that geometrical-barrier effects are enhanced by the Bean-Livingston barrier.