3.38 Sspd_chapter 1_part 15_quantum fluids_superconductivity &  (Page 6/6)

In metals above T _C the electron gas is a fermionic system. At temperatures below T _C the fermionic electron gas is abruptly condensed into an assembly of boson molecules called cooper pairs of electrons. These cooper pairs experience BOSON CONDENSATION in an analogous manner as in He-II phase and manifest a complex of spectacular properties characteristic of a super-conductor namely:

1. the electrical resistance becomes zero. If a super conducting ring is cooled below the transition temperature and magnetic field linking the coil is varied for a short period of time then a current is induced and it continues to flow in the super-conducting ring for time immemorial. In super-conductors the usual scattering mechanisms are rendered ineffective just as in He-II the frictional effect of the walls of the container are rendered inoperative;
2. ‘Meissner Effect’- that is the total exclusion of magnetic flux from a super conducting body. By Lenz’s law of electromagnetic induction, electro magnetic force (e.m.f.) induced in a conductor is proportional to the rate of change of magnetic flux linking the conductor and the direction of the e.m.f. and the consequent eddy current is such as to oppose the cause of change. If the change of flux is increasing the eddy current will produce an opposing magnetic field and if the change of flux is decreasing then the eddy current will produce an aiding magnetic field. In effect the eddy current tends to shield the conductor from a change of flux. In ordinary conductors the eddy current ebbs out in seconds and the shielding effect vanishes in the same time scale and the magnetic field assumes the new steady state value of the magnetic field. But in astrophysical objects the eddy current and the shielding effect persists for several thousand years. In super-conductor since the resistance is zero, the eddy current persists for ever and continues to exclude the magnetic flux for time immemorial. Effectively a superconductor behaves as a dia-magnetic material;
3. Magnetic Levitation- this is a direct consequence of Meissner Effect. In the process of excluding the magnetic field the superconductor experiences a force of repulsion. If a superconductor is held over the north pole or south pole of a magnet, the former will be held hanging in the mid-air because the gravitational force on the freely falling body is exactly counter-balanced by the force of repulsion due to field exclusion;
4. Magnetic Flux Quantization- If a ring of superconductor is placed in a magnetic field then the field excluded from the annular part of the ring but is included through the central hole of the ring. The flux linking the central hole is an integral multiple of h/e = 10 ^-15 Weber i.e. φ = n(h/e) where n is an integral number. The flux passage through a normal non-magnetic conductor, the magnetic flux exclusion by the superconductor and the partial linkage through a super-conductor ring is shown in Figure (1.85).

Figure 1.85. Behaviour of a piece of superconducting metal in a magnetic field.

1. Above the transition temperature when the metal is normal and the sample is completely penetrated by the field ( whatever its shape is),
2. Below T c when it is super conducting, a spherical sample completely excludes the field,
3. For a ring shaped specimen in the super-conducting state, some of the field lines can go through the central hole of the ring but always as an integral multiple of (h/e).

The theory of cooper pairs and the formation of cooper pairs in isotropic state explains only ‘Very low temperature’ super conductors. There is a class of heavy fermion superconductors as well as high temperature ceramic superconductors which cannot be explained by the present theory.