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 $\mathbf{B}$, unless $\mathbf{B}$ is in a crystal-symmetry direction. In general, the mean-field free energy is thus a function of a new parameter $\beta$, which depends upon the direction cosines of $\mathbf{B}$, as well as a function of the renormalized $\tilde{\kappa }$ parameter of I, except at the upper critical field $H_{c2\mathrm{}}$. A perturbation solution in $\gamma =\frac{\beta }{(1+\beta )}$ is found to order ${\gamma }^2$, and the angular dependence of the lower critical field $H_{c1\mathrm{}}$ is determined. The parameter $\beta$ is found to cause $\mathbf{B}$ to nearly lock on to a crystal-symmetry direction, so that as the external field angle is varied, $\mathbf{B}$ switches from near to one symmetry direction to (near to) another, yielding a kink in the angular dependence of $H_{c1\mathrm{}}$ that is more pronounced than in I.