1.11 Type II superconductors Ë 15In type II superconductors, [22, 23] increasing the applied field more than the
lower critical fieldHc1forces 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, sometimes 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 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 length휉and a surrounding
outer region with radius equal to the penetration depth휆, where superconducting
screening currents flow around the core in the thin layer휆. Its behavior is analogous
to the exponential decay [see Eq. (1.22)] in type I superconductors. In applied fields
H(Hc1<H<Hc2), the density of vortices is approximately proportional to the applied
field.
When the superconductor carries a currentI, the flux lines experience a Lorentz
force:
FL=I×B, (1.45)
whereB=휇 0 H. Under this Lorentz forceFL, the flux lines start to move through the
lattice if it overcomes the pinning forceFPof the lattice. If the pinning forceFPis
stronger than the Lorentz forceFL, i.e. at temperatures far belowTc, 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 forceFLis larger than the pinning forceFP, the flux line lattice
will be driven by the Lorentz forceFLand 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 densityJc. 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