Dear Jothsana .S,

You may want to look over info below:

Vortices in type-II superconductor arise when the magnetic field starts to penetrate the materials in the form of quantized flux. The vortices interact with each and can form different phases under the influence of the magnetic field, thermal fluctuations, and the pinning effect of disorder and defects. As the usual theoretical methods towards vortex matter, the London model is briefly introduced while the Ginzburg-Landau models are discussed at length for their capability of describing more interesting phases of the vortices. Some experimental techniques of measuring the vortices are also mentioned at the end of the term essay.

https://guava.physics.uiuc.edu/~nigel/courses/569/Essays_Fall2012/Files/yu.pdf

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The origin of the vortex-core states in s-wave and dx2−y2-wave superconductors is investigated by means of some selected numerical experiments. By relaxing the self-consistency condition in the Bogoliubov–de Gennes equations and tuning the order parameter in the core region, it is shown that the suppression of the superfluid density in the core is not a necessary condition for the core states to form. This excludes “potential well” types of interpretations for the core states. The topological defect in the phase of the order parameter, however, plays a crucial role. This fact is explained by considering the effect of the vortex supercurrent on the Bogoliubov quasiparticles and illustrated by comparing conventional vortices to multiply quantized vortices and vortex-antivortex pairs. The core states are also found to be extremely robust against random disorder of the phase.

https://www.researchgate.net/publication/235463324_Vorticity_and_vortex-core_states_in_type-II_superconductors

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In type I superconductors a magnetic field is not allowed to penetrate at all

(Meisner effect) and because of magnetic pressure you can suspend or float such supercoductor in a magnetic field. Beyond some critical magnetic field the material becomes normal

In a type II such as the ceramic type ,the penetration of the magnetic field becomes partial by the penetration of an array of vortices in which the magnetic flux is

quantized (has certain discrete values)

When a superconductor is cooled through Tc (superconducting transition temperature) in the presence of a magnetic field, the magnetic lines of force, which pass through the solid, disappear below a critical magnetic field H_c. In other words, the magnetic induction B is zero inside the solid in the superconducting state. It is called Meissner effect. Type I superconductors obey Meissner effect completely. In type II superconductors, however, there are two critical fields, H_c1 and H_c2. Suppose H is the applied magnetic field. For H< H_c1, the material is a superconductor. For H>H_c2, it is a normal conductor. For H_c1

@Gouri S.Tripathi

Sir,Is there any advantage or disadvantage of this vortex state

The following information could be of some relevance in view of your query. In the vertex state, because of flux pinning, a magnetic field can be trapped, leading to the magnetic lavitation. It is a frictionless state and could be used for frictionless joints and bearings.

The most useful and widely employing application of pinned vortex ensamble is superconducting wires for all types of SC magnets and other SC winding, SC cables for energy transmition and so on.

Vortex stat is the state at which superconductivity and magnetism coexist. It is very important for applications.