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

We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $γ_λ(T)$. 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 $Δ(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $Δ(T)/Δ(0)$ 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 $γ_λ(T)$. Of particular interest is mixed order parameters of two symmetries for which $γ_λ(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $Δ_{max}(0)/T_c$ 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 $Δ$.

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