Ginzburg-Landau vortex lattice in superconductor films of finite thickness

Ernst Helmut Brandt

doi:10.1103/PhysRevB.71.014521

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Ginzburg-Landau vortex lattice in superconductor films of finite thickness

Ernst Helmut Brandt

DOI 10.1103/PhysRevB.71.014521 · Physical Review B

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Abstract

The Ginzburg-Landau equations are solved for ideally periodic vortex lattices in superconducting films of arbitrary thickness in a perpendicular magnetic field. The order parameter, current density, magnetic moment, and the three-dimensional magnetic field inside and outside the film are obtained in the entire ranges of the applied magnetic field, Ginzburg-Landau parameter κ, and film thickness. The superconducting order parameter varies very little near the surface (≈1%) and the energy of the film surface is small. The shear modulus c66 of the triangular vortex lattice in thin films coincides with the bulk c66 taken at large κ. In thin type-I superconductor films with κ<1∕2,c66 can be positive at low fields and negative at high fields. The magnetization of thin films at small applied fields is enhanced beyond its bulk value −Hc1 due to the energy of the magnetic stray field.