14 Ë 1 Fundamentals of superconductivity
The upper critical fieldHc2( 0 )of a type II superconductor is very high so that direct
measurement is not realistic; however, it can be estimated using the slope ofHc2with
increasing temperature, the approximate formula is [16]
Hc2= 0. 69 Tc儨儨儨
儨儨儨
儨儨
dHc2
dT儨儨儨
儨儨儨
儨儨T=Tc. (1.42)For HTSC with planar structure, the critical magnetic fields are larger when the
external field applied is perpendicular to thec-axis than when it is applied parallel
to this axis.
1.10 Type I superconductors
Superconductors can be categorized into two classes, types I and II. The ratio (1.30) of
the penetration depth휆to the superconducting coherence length휉is called as the GL
parameter휅, which determines whether a material is type I or type II superconductor.
For type I superconductors, this ratio is
0 <휆/휉< 1 /$ 2 , (1.43)
and for type II superconductors,
휆/휉> 1 $ 2. (1.44)
Most pure elemental superconductors, except niobium and carbon nanotubes, are
type I superconductors, while almost all impure and compound superconductors
are type II superconductors. Type 1.5 superconductor refers to a multicomponent
superconductor which is characterized by two or more coherence lengths, and
휉 1 <$ 2 휆<휉 2.
Superconducting materials that completely expel magnetic flux until they become
completely normal are called as type I superconductors. The superconductor is in
the Meissner-Ochsenfeld state at small magnetic field. The Meissner-Ochsenfeld state
breaks down when the applied magnetic field has a certain larger value.
1.11 Type II superconductors
Type II superconductors [4, 9, 21] have two critical fields, the lower critical magnetic
fieldHc1and the upper critical magnetic fieldHc2, between which they allow partial
penetration of the magnetic field.