Two-band effect in superconducting parameters and their anisotropies of $MgB_2$ single crystals

$MgB_2$ 단결정의 초전도 상수와 그 이방성에 나타난 두 개의 띠의 영향

We have studied superconducting parameters of $MgB_2$ single crystals from reversible magnetization measurements with the magnetic field both parallel and perpendicular to the c-axis of the crystals. The temperature dependence of the London penetration depth, ${\lambda}_{ab}{^{-2}}(T)$, obtained from the Hao-Clem analysis on reversible magnetization, shows a clear discrepancy from single-band theories. It is also found that the anisotropies of the London penetration depth, ${\gamma}_{\lambda}$, slowly increases with temperature while the anisotropy of the upper critical field, ${\gamma}_H$, decreases with temperature. These behaviors are in sharp contrast with the behavior of superconductors with a single band. The temperature dependence of ${\lambda}_{ab}{^{-2}}$, and the opposite temperature dependences of ${\gamma}_{\lambda}\;and\;{\gamma}_H$ can be well explained with the theory of the two-band superconductivity.