Anisotropy parameters of superconducting MgB$_2$

Abstract

Data on macroscopic superconducting anisotropy of MgB$_2$ are reviewed. The data are described within a weak coupling two-gaps anisotropic s-wave model of superconductivity. The calculated ratio of the upper critical fields $\gamma_H=H_{c2,ab}/H_{c2,c}$ increases with decreasing temperature in agreement with available data, whereas the calculated ratio of London penetration depths $\gamma_{\lambda}=\lambda_c/\lambda_{ab}$ decreases to reach $\approx 1.1$ at T=0. Possible macroscopic consequences of $\gamma_{\lambda}\ne\gamma_H$ are discussed.