4 Ë 1 Fundamentals of superconductivity
below a critical field when the temperature is below the critical temperatureTc.
This important property allows us to distinguish a superconducting material from a
perfect conductor.
According to Lenz’s law, when a changing magnetic field is applied to a conductor,
it will induce an electric current in the conductor that creates an opposing magnetic
field. However, the Meissner-Ochsenfeld effect is the spontaneous expulsion which
occurs during the transition to the superconducting state. Suppose there is a super-
conductor in the normal state placed in a constant external magnetic field. When
it is cooled below the critical temperatureTc, the abrupt expulsion of the internal
magnetic field would occur, which is not expected based on Lenz’s law.
The dimensionless magnetic susceptibility is defined as휒=M/H, and the magne-
tic flux density can be expressed as
B=휇 0 H( 1 +휒)=휇 0 (H+M), (1.1)while휇 0 is the permeability of free space. The property of perfect diamagnetism means
that the susceptibility휒= −1, i.e. the magnetizationM= −H, so there can be noBfield
inside a superconductor.
If a superconductor in the normal state is cooled belowTcby zero field-cooled
(ZFC) method, the normal state to the superconducting state transition happens
without the presence of any magnetic field. Thereafter, the cooled superconductor is
placed in an external magnetic field, and the magnetic field will be expelled from the
superconductor. If this superconductor in normal state is placed in an external magne-
tic field, the field will penetrate and have the same value inside and outside. When a
superconductor in the normal state is cooled below itsTcby field-cooled (FC) method,
the normal state to the superconducting state transition happens with the presence of
a magnetic field; thereafter, the field will be expelled from the superconductor. This
phenomenon of superconductors is named as the Meissner-Ochsenfeld effect, and a
similar phenomenon cannot be found in conventional conductors and demonstrates
that superconductivity is a new thermodynamic phase.
The superconductors that totally exclude applied magnetic flux are known as type
I superconductors. The Meissner-Ochsenfeld effect exists in type I superconductors
below the critical fieldHc, but the superconductivity will be destroyed aboveHc.
In type I superconductors whose thicknesses are much greater than the penetration
depth휆, internal magnetic fields and transport currents are merely able to exist only
in a surface layer of thickness휆.
The magnetic properties of type II superconductor are more complex. type II
superconductors are similar to type I superconductors but the presence of a Meissner-
Ochsenfeld effect only happens when the magnetic applied field is smaller than
a lower critical fieldHc1. When the applied magnetic field is higher thanHc1but
lower than its upper critical fieldHc2, magnetic vortices begin to penetrate into the
superconductor and the material enters the mixed state. The magnetic field can