Theory of the Mixed State of MgB 2

1. GL asymptotics s-band Large length scale for the p-band DoS Small field scale Theory of the Mixed State of MgB2 A. E. Koshelev (MSD ANL) and A. A. Golubov (Univ. of Twente, the Netherlands) We investigate two-band properties of the vortex state in magnesium diboride (MgB2) within a microscopic model: a two-band superconductor with strong intraband and weak interband scattering. For field along c-direction we compute the pair potentials and local densities of states for two bandsfor an isolated vortex and find their field evolution. The existence of two distinct length and field scales corresponding to different bands is demonstrated. We calculate the upper critical field for different field orientation. Due to a large difference between the c-axis coherence lengths in two bands, the GL theory does not describe properties of this superconductors: the Hc2 anisotropy has strong temperature dependenceand the angular dependence of Hc2 strongly deviates from a simple effective-mass law. Upper critical field Two-band superconductivity in MgB2: quasi-2D strongly superconductings-bands, Ds≈ 7 meV 3D p-bandswith induced superconductivity, Dp≈ 2.2 meV Two-band features in the properties of mixed state ? Model: Two-band Usadel equations Input:coupling constantsLab. diffusion constantsDa,j,a =(1,2)=(s,p)band index Output: pair potentials Da(r); Observable properties: partial local DoS Na(E,r), upper critical fields Hc2(Q,T) … Temperature dependence of the upper critical field in the a-direction (red solid), single-band curve (green dashed), and GL asymptotics (blue dotted). Inset: temperature dependence of the anisotropy parameter. Vortex state for H along c axis STM imaging of vortices in MgB2,Eskildsen et al.Phys. Rev. Lett. 89, 187003 (2002) [tunneling to p-band] • Features: • Almost at all temperatures both Hc2,c and Hc2,a are mainly determined by the strong s-band • p-band strongly suppresses Hc2,a only invery narrow GL regionin the vicinity of Tc leading to temperature-dependent anisotropy. Angular dependence of Hc2 Large vortices: xv » xc2 Effective-mass (AGL) angular dependence Hc2(q) Theory:Isolated Vortex Deviations from the AGL angular dependence temperatures not very close to Tc temperature region near Tc Spatial dependencies of pair potentials,Da(r), and partial DoS atE=0, Na(0,r), for D1 = 0.2D2. Partial DoS in p-band, 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 See Poster XX for comparison with experiment !!! Breakdown of anisotropic Ginzburg-Landau theory Future direction: Fluctuations in two-band superconductors Temperature dependence of c-axis coherence length xz 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. Collaboration with A. Varlamov (Univ. of Roma, Italy) We will develop theory of fluctuations for MgB2. Since the standard GL approach fails in description of its properties, we will generalize it basing on the microscopic theory. We will derive the nonlocal two-band GL functional which will allow us to calculate the main fluctuation observables such as fluctuation specific heat and conductivity. A. E. Koshelev and A. A. Golubov, Phys. Rev. Lett. 90, 177002 (2003); Phys. Rev. B 68, 104503 (2003); Phys. Rev. Lett. 92, 107008 (2004). FWP 58906 This work was supported by the U. S. Department of Energy, Basic Energy Sciences, under contract W-31-109-ENG-38.