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

TL;DR

This paper investigates how anisotropic superconducting order parameters influence the temperature dependence of London penetration depth anisotropy, revealing effects in one-band materials and complex behaviors in mixed symmetry states.

Contribution

It demonstrates that anisotropic order parameters can cause temperature-dependent anisotropy in single-band superconductors and provides a simplified interpolation method for evaluating this dependence.

Findings

Anisotropy parameter varies with temperature in one-band superconductors with anisotropic gaps.

A simplified interpolation accurately models the temperature dependence of the order parameter.

Mixed order parameters can lead to a maximum in anisotropy and a ratio of maximum gap to critical temperature exceeding the weak coupling limit.

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 $\Delta$.