12 Ë 1 Fundamentals of superconductivity
The GL critical current density is expressed as [20]Jc= 훷^0
3 $ 3 휋휇 0 휆^2 휉. (1.35)
According to Eqs. (1.24) and (1.42),
Jc(T)=Jc( 0 ) 1 −T
Tc
2
¡ 1 −T
Tc
4
¡1 / 2. (1.36)
Since the current of a type I superconductor is concentrated within the penetration
depth of the surface, the critical current of a type I superconductor wire is direct-
ly proportional to the outer circumference of superconducting wire. For a type II
superconductor which works in a mixed state betweenHc1andHc2for practical
applications, the distribution of the superconducting current is more complicated.
For HTSC with planar structure, the critical current densities are smaller when the
external field is applied perpendicular to thec-axis than when applied parallel to the
axis. [20]
1.9 Critical magnetic fields
A superconductor in a sufficiently strong magnetic field will return from the super-
conducting state to the normal state. This field is named as the critical magnetic
fieldHc. For type II superconductors, the upper critical magnetic fieldHc2depends
on the vortex structure. For type I superconductors, the superconducting state can
be destroyed by the thermodynamic critical magnetic fieldHc. The critical magnetic
field increases as temperature is lowered and reaches the maximum value atT=0 K.
Generally, the thermodynamic critical fieldHcis lower thanHc2for type II.
The superconducting state can also be destroyed by the self-field from a large
transport current through the material. This maximum transport current is the so-
called critical current densityJc(see section 1.8). It depends on the properties and the
geometry of the superconductor. Both the critical currents and the critical magnetic
fields are directly related to the temperature. With lower temperature, the better
property is achieved. This critical magnetic field is also a very important parameter
for industrial applications.
Type I superconductors have a single critical fieldHc, above which supercon-
ductivity vanishes. Type II superconductors have two critical fields, the lower critical
magnetic fieldHc1, and the upper critical magnetic fieldHc2, between which they allow
partial penetration of the magnetic field in the form of magnetic vortices.
The splitting energy level of the electron ground state in a magnetic field is called
as the Zeeman splitting energy level. When the Zeeman splitting energy levelΔEof