Angular dependence of the upper critical field in layered superconductors

The upper critical field, H_c2(θ), in layered superconductors is investigated in an arbitrary direction θ, using a Ginzburg-Landau model proposed in a previous paper. Here, θ is the angle measured from the direction perpendicular to the layers. The angular dependence of H_c2(θ) in the region near θ=90° is correlated with the dimensionality in the temperature dependence of H_c2 (90°). We have a bell-shaped curve in the 3D regime and a curve with a cusp at θ=90° in the 2D regime in the H_c2 versus θ curve. The global angular dependence of H_c2(θ) in layered superconductors shows a clear difference from that in a 2D thin film and also from that in the anisotropic effective mass model. The behavior of H_c2(θ) in the small θ region is well understood on the basis of the proximity effect in layered superconductors. Qualitatively, the calculated result for H_c2(θ) reproduces well the angular dependence observed in Nb/Cu multilayers with various layer thicknesses.