# Presentation: 449854

## Theory of the Mixed State of MgB2

***Theory of the Mixed State of MgB******2***

**A. E. Koshelev (MSD ANL) and A. A. Golubov (Univ. of Twente, the Netherlands)**

**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).**

**This work was supported by the U. S. Department of Energy, Basic Energy Sciences, under contract W-31-109-ENG-38.  **

*FWP 58906*

- 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 bands for 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 dependence and the angular dependence of Hc2 strongly deviates from a simple effective-mass law.

- Two-band superconductivity in **MgB****2**:
- 	quasi-2D strongly superconducting -bands,  ≈ 7 meV
-        3D -bands with induced superconductivity,  ≈ 2.2 meV
- Two-band features in the properties of mixed state ?

_**Model:**__** Two-band Usadel equations**_

**Input:** coupling constants . diffusion constants D,j, =(1,2)=(,) band index
**Output**: pair potentials (r) Observable properties: partial local DoS N(E,r),
-          upper critical fields Hc2(,T) ...

_**Vortex state for H along **__***c***__** axis**_

_**Theory:**_** **_**Isolated Vortex**_

- Spatial dependencies of pair potentials, (r), and partial DoS at E=0, N(0,r), for *D*1 = 0.2*D*2. Partial DoS in -band, probed by STM, has large length scale.

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

- STM imaging of vortices in MgB2,  Eskildsen et al. Phys. Rev. Lett. **89**, 187003 (2002)
- [tunneling to -band]

- Large vortices: v  » c2

- 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.

_**Upper critical field**_

- _Features:_
- Almost at all temperatures both Hc2,c and Hc2,a are mainly determined by the strong -band
- -band strongly suppresses Hc2,a only in* **very narrow GL region** *in the vicinity of Tc leading to temperature-dependent anisotropy.

-  temperatures not very close to Tc

-  temperature region near Tc

- Effective-mass (AGL)
- angular dependence Hc2()

- See Poster XX   for comparison with experiment !!!

_**Angular dependence of H**__**c2**_

_**Deviations from the AGL angular dependence**_

_**Breakdown of anisotropic Ginzburg-Landau theory**_

- Due to the band structure of MgB2, the anisotropic GL theory does not have practical applicability range: -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.

- Temperature dependence of c-axis coherence length z

_**Future direction:**__** Fluctuations in two-band superconductors  **_

- 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.