Anisotropy in mixed superconducting state of two-band MgB2 superconductor

The multi-band superconductor MgB2 exhibits two-dimensional σ-band superconductivity and three-dimensional π-band superconductivity. We investigate the electronic anisotropy in MgB2 by doing systematic magnetic torque measurements under various different temperatures and magnetic fields. The Kogan theory for single-band superconductors explains the properties of a variety of anisotropic superconductors in terms of the anisotropy γλ in penetration depth λ, but it fails to explain the MgB2 torque successfully in some cases. The two-band version of the Kogan torque theory is needed to give a better description of the MgB2 torque curve. The γξ value coming from the anisotropy in coherence length ξ plays an important role in a multi-band superconductor. We consider that the suppression of γξ in MgB2 derived here comes from enhanced σ-π mixing between two-band carriers.