Amount of flux lines 'pinned' in type II superconductor

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SUMMARY

The discussion focuses on the relationship between magnetic fields and the density of vortices in type II superconductors. It establishes that the magnetic field affects the number of fluxons present, with the equation N*(flux quantum)/(macroscopic area)=B_ext defining the relationship between vortex density and external magnetic field. In ideal conditions without defects, vortices can form ordered lattices, typically hexagonal or square, which can be analyzed through decoration experiments, neutron scattering, or electron microscopy to calculate density.

PREREQUISITES
  • Understanding of type II superconductors and their properties
  • Familiarity with quantum vortices and flux quantization
  • Knowledge of lattice structures in condensed matter physics
  • Experience with experimental techniques such as neutron scattering and electron microscopy
NEXT STEPS
  • Research the mathematical modeling of vortex density in type II superconductors
  • Explore the effects of defects and pinning centers on vortex behavior
  • Learn about decoration experiments for visualizing vortex lattices
  • Investigate the implications of vortex lattice structures on superconducting properties
USEFUL FOR

Physicists, materials scientists, and engineers interested in superconductivity, particularly those studying vortex dynamics and lattice structures in type II superconductors.

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a type II superconductor may not exhibit complete exclusion of magnetic field due to quantum vortices. It is my understanding that the magnetic field present will affect the number of vortices or fluxons present, but what is the relationship between magnetic field, and number of vortices in a type II superconductor (zero-field cooled), or am I completely missing the mark?
 
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Graphically, you can imagine that the magnetic fields lines of the external field are "bundled" into quantized packets inside the superconductor.

The density of vortices is then such that the macroscopic flux is the same as outside of the SC, N*(flux quantum)/(macroscopic area)=B_ext, where N is the number and N/(macroscopic area) is the density of vortices.

In the absence of defects and pinning centers, the vortices may form ordered lattice. In most materials these are hexagonal, but square ones also occur. These lattices can be observed with decoration experiments, neutron scattering or electron microscopy. From the lattice parameters you can calculate the density.
 

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