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Study of Abrikosor Vortex lattice and evaluation of (K1⁄K) and (K2⁄K) as a function of reduced temperature (T⁄Tc)c for for Nb - T1 superconductor

Shambhoo Nath Prabhakar

Department of Physics,
Mahila College, Tekari (Gaya), Vill : Andhar : P.O- Makhdumpur- 824232, INDIA.

ABSTRACT

Type- I Superconductor are superconductors that exhibit zero resistance and perfect diamagnetism. They are perfect diamegnets for applied magnetic fields below the critical field Bc and becomes normal for higher applied fields. Their coherence length exceeds their penetration depth (ξ > λ) so it is not energically favourable for boundaries to form between their normal and superconducting phase. The superconducting element with the exception of Niobium, are all type I. When the penetration depth λ is larger than the coherence length ξ, it becomes energetically favorable for domain walls to form between the superconducting and normal regions. When such a superconductor, called type II, is in a magnetic field, the free energy can be lowered by causing domains of normal material containing trapped flux to form with low energy boundaries created between the normal core and the surrounding superconducting material. When the applied magnetic field exceeds a value referred to as the lower critical field, BC1, magnetic field is able to penetrate in quantized units by forming cylindrically symmetrical domains called vortices. For applied fields slightly above BC1 the magnetic field inside a type II superconductor is strong in the normal cores of the vortices, decreases with distance from the cores, and becomes very small far away for much higher applied field the vortices overlap and the field inside the superconductor become strong everywhere. Eventually, when the applied field reaches a value called the upper critical field BC2, the materials becomes normal. Alloys and compounds exhibit type II superconductivity with mixed type magnetic behavior and partial flux penetration above BC1. Type II superconductors also have zero resistance, but their perfect diamagnetism occurs only below the lower critical field BC1. Then one defines the ratio of λ and ξ as a Ginzburg-Landau parameter κ. κ plays a very important role in type II superconductors. The density of super electron ns which characterizes the superconducting state, increase from zero at the interface with a normal material to a constant value for inside, and the length scale for this to occur is the coherence length ξ. As external magnetic field B decays exponential to zero inside a superconductor. For type I superconductor for coherence length is the larger of the two length scales, so superconducting coherence is maintained over relatively large distance within the sample. The overall coherence of the superconducting electrons is not disturbed by the presence of external magnetic fields.

Keywords : Superconductivity, super current, vortex lattice, Gibbs energy.