1.11　Type II superconductors

Type II superconductors4，9，21have two critical fields, the lower critical magnetic field Hc1and the upper critical magnetic field Hc2 ，between which they allow partial penetration of the magnetic field.

In type II superconductors22，23，increasing the applied field to be higher than the lower critical field Hc1 forces the superconductors to enter the mixed state（namely the vortex state）. In the mixed state, the normal state exists in the cores of the vortices and the superconducting state coexists outside the cores.With an increasing amount of magnetic flux that penetrates into the material, there remains no resistance to the flow of superconducting current if the current is not too large.The mixed state is actually caused by the vortices in the electronic superfluid, some times called fluxons since the amount of flux carried by these vortices is quantized.The vortices play a very special role in applications of type II superconductors.

In the mixed state, the magnetic fluxes parallel to the external magnetic field penetrates within a cylinder. The cylinder is called as the normal core.The normal vortex cores in the mixed state are surrounded by superconducting regions.Vortex shielding currents are formed around the normal core, and the magnetic field is gradually shielded.The circulating vortex shielding current generates and maintains the flux line in the normal core.The magnetic flux is the magnetic flux quantum.

The vortices have a core radius equal to the coherence length ξ and a surround ing outer region with radius equal to the penetration depthλwhere supercon ducting screening currents flow around the core in the thin layerλ.Its behavior is analogous to the exponential decay[see Eq.（1.6.1）]in type I superconductors.In applied fields H（Hc1 ＜H＜Hc2 ），the density of vortices is approximately propor tional to the applied field.

When the superconductor carries a current I, the flux lines experience a Lorentz force：

where B=μ0 H.Under this Lorentz force FL the flux lines start to move through the lattice if it overcomes the pinning force FP of the lattice.If the pinning force FP is stronger than the Lorentz force FL ，i.e.at temperatures far below Tc , the flux line lattice is pinned by the pinning center.However, thermal fluctuations will cause some vortices to escape from the pinning center.This phenomenon is named as flux creep.However, if the Lorentz force FL is larger than the pinning force FP ，the flux line lattice will be driven by the Lorentz force FL and move.This phenomenon is named as flux flow.The motion of vortices generate energy dissipation because the vortex cores are in the normal state.

In an ideal type II superconductor there is nothing to hinder the motion of flux lines. Since the magnetic gradient cannot be formed due to the absence of pinning centers, this leads to a vanishing critical current density Jc .Such superconductors have little value for applications.

In a real superconductor, there are always lattice defects or impurities and small particles which serve as pinning centers for the flux line lattice. The pinning centers play an important role to prevent the flux line from motion.The better the flux pinning properties, the higher the critical current density.When the magnetic field is sufficiently strong, the flux becomes free from the pinning and can move freely.This magnetic field is called as the irreversible field Hirr, and it is one of the im portant parameters for superconducting applications.At the irreversible field Hirr the critical current density reduces to zero.The irreversible field Hirr is determined by the mechanism of flux creep, and can be derived from the E-J characteristics caused by the flux creep24.As the critical temperature is approached, the normal cores are more closely packed and eventually overlap so that the superconducting state is lost.At this upper critical field Hc2 ，superconductivity is destroyed.

To avoid the motion of vortices and thus ensure zero resistance of a super conductor, various defects such as granular structure, lattice defects, or artificial defects are introduced into the superconducting material. Each defect attracts vor tices, and these vortices produce a series of pinning centers in the superconductor.Below the critical current density Jc , a hard type II superconductor can have zero resistance up to very high magnetic fields.The high magnetic field is not Hc2 ，but is the irreversible field Hc3 and Hc1 ＜Hc3 ＜Hc2 .

In HTSC are limited by the irreversibility field Hc3 above which magnetic vor tices melt or decouple. Even though BSCCO has a higher upper critical field Hc2 than YBCO it has a much lower Hc3 （typically smaller by a factor of 100）thus limiting its use for making high-field magnets.It is for this reason that conductors of YBCO are preferred to BSCCO.