Theory of multiband superconductors

Collaborator: Alexander Golubov (Univ. of Twente, The Netherlands )
The multigap superconductivity in the recently discovered compound magnesium diboride (MgB₂) has been theoretically predicted and confirmed by many experiments. Superconductivity in MgB₂ resides in two distinct groups of bands: strongly superconducting quasi-2D s-bands and weakly superconducting 3D p-bands. Intraband impurity scattering in both bands may vary in large limits, while interband scattering remains weak. The two-gap superconductivity in MgB₂ persists even in the intraband dirty limit.

We investigate a simple microscopic model of MgB₂, a two-band superconductor with strong intraband and weak interband electronic scattering rates. Such superconductor is described by Usadel equations coupled via the self-consistency conditions. Model is defined by: matrix coupling constants l_ab and diffusion tensors for two bands D_a,a. In the case of magnetic field applied along c direction we solved coupled nonlinear Usadel equations numerically to find field evolution of the pair potentials and local densities of states [DoS] for two bands. We demonstrate the existence of two distinct length and field scales corresponding to different bands.

For details see: Phys. Rev. Lett., 90, 177002 (2003),

Spatial dependencies of partial DoS at zero energy  for D1,x = 0.2D2,x. Partial DoS in p-band, N2(0,r), probed by STM, has large length scale.

Field dependencies of pair potentials and averaged DoS at E=0. p-band DoS reaches the normal value at small field scale

Due to the band structure of MgB2, the anisotropic GL theory does not have practical applicability range: p-band induces strong nonlocality along c-direction. We derive a “minimum model” which takes into account this nonlocality and replaces the usual GL theory in the vicinity of transition temperature. For details see: Phys. Rev. Lett., 92, 107008 (2004).

Temperature dependence of c-axis coherence length xz

We calculate the upper critical field, H_c2, for different field orientation. Due to breakdown of the Ginzburg-Landau theory  the H_c2 anisotropy has strong temperature dependence and the angular dependence of H_c2 strongly deviates from a simple effective-mass law. Both predicted properties have been confirmed experimentally. 

For details see:  Phys. Rev. B, 68, 104503 (2003),