Lower critical field of an anisotropic extreme type-II superconductor

It is shown that the procedure of Klemm and Clem (abbreviated as I) for the transformation to isotropic form of the Ginzburg-Landau free energy for a superconductor with a general effectivemass anisotropy leads to a current which is not perpendicular to the magnetic induction B, unless B is in a crystal-symmetry direction. In general, the mean-field free energy is thus a function of a new parameter β, which depends upon the direction cosines of B, as well as a function of the renormalized ̃ \~κ parameter of I, except at the upper critical field Hc2. A perturbation solution in γ=β(1+β) is found to order γ², and the angular dependence of the lower critical field Hc1 is determined. The parameter β is found to cause B to nearly lock on to a crystal-symmetry direction, so that as the external field angle is varied, B switches from near to one symmetry direction to (near to) another, yielding a kink in the angular dependence of Hc1 that is more pronounced than in I.