Superconductors vortex state

Figure 13.16 Magnetization verses applied magnetic field for (a) a type I superconductor and (b) a type II superconductor. For the type I superconductor, the magnetic flux does not penetrate the sample below 9 Cc where the sample is a superconductor. Above rMc, the sample is a normal conductor. For the type II superconductor, the magnetic field starts to penetrate the sample at 3Cc, 1, a magnetic field less than rXc, the thermodynamic critical field. Superconductivity remains in the so-called vortex state between 9 c and Ci2 until WCt2 is attained. At this magnetic field, complete penetration occurs, and the sample becomes a normal conductor.

Type 2 This behaviour is not so clear cut. At small values of the applied field, the material behaves in the same way as a type 1 superconductor and there is not penetration by the field. Similarly, at high values of the applied field the field readily penetrates the whole sample. However, at intermediate values, between the two extremes, there is partial penetration by the field and the sample exhibits a complex structure. There are mixed regions in the superconducting and normal state. This is known as the vortex state. This means that in type 2 materials the magnetization diminishes gradually rather than suddenly (Figure 5.28)... 

Figure 2-4. Magnetization versus applied magnetic field for a type II superconductor. The flux starts to penetrate the specimen at a field Wei lower than the thermodynamic critical field The specimen is in a vortex state between Wei and Wc2 and it has superconducting electrical properties up to We2. (From Kittel [18].)...

Fig. 13. Analogous phase diagrams for the Vortex state in superconductors and the screw...

For each vortex state a specific resistivity-current relation exists, as schematically shown in Fig. 4.2-20. A linear relation occurs for the flux flow regime only. Therefore a voltage criterion for the critical current has to be defined. The one generally used is 1 xV cm . Extensive reviews of the structure and behavior of vortices in high-7i superconductors are given in [2.19,20]. 

An interesting question is whether the subtle effects of non-locality and, in particular, the hexagonal-square transition of the vortex lattice would be preserved in the superconducting state of magnetic superconductors such as / Ni2B2C with R = Er and Tm. 

From here follow main goals in the SIT problem to find theoretical models which would lead to the negative magnetoresistance to trace how the specific SIT properties appear in the field-induced superconductor-normal metal transition while the normal metal is shifted toward the insulating state to find out whether the low dimensions of the films is crucial or the SIT can happen in 3D materials to find the explanation for the pair localization alternative to the boson-vortex duality. It seems that the first two goals are achieved. 

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