Temperature dependence of London penetration depth anisotropy in superconductors with anisotropic order parameters

Abstract

We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $\gamma_\lambda(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $\Delta(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $\Delta(T)/\Delta(0)$ can be represented with good accuracy by the interpolation suggested by D. Einzel, J. Low Temp. Phys, {\bf 131}, 1 (2003), which simplifies considerably the evaluation of $\gamma_\lambda(T)$. Of particular interest is mixed order parameters of two symmetries for which $\gamma_\lambda(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $\Delta_{max}(0)/T_c$ may exceed substantially the weak coupling limit of 1.76. It, however, does not imply a strong coupling, rather it is due to significantly anisotropic angular variation of $\Delta$.