On temperature-dependent anisotropies of upper critical field and London penetration depth

We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies $gamma_H$ of the upper critical field and $gamma_lambda$ of the London penetration depth depend on temperature, the feature commonly attributed to multi-band superconductors. The parameters $gamma_H$ and $gamma_lambda$ may have opposite temperature dependencies or may change in the same direction depending on Fermi surface shape and on character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, anisotropies, and order parameters. We investigate in detail the conditions determining the directions of temperature dependences of the two anisotropy factors.