Question

Solis state Physics:

How BCS theory explained the phenomenon exhibited by superconductor like Messner effect, flux quantisation and the other one(if there are).

Answer 1

Superconductor

the materials that conduct electricity with no resistance at the temperature below a Critical Temperature T_c.

[ Critical temparature is the temperature above which the conductor becomes as superconductor]

BCS Theory [ Scientists :John Bardeen, Leon Cooper, Robert Schriffer]

The phenomenon of superconductivity involves uinteraction between the electrons and the vibrating lattices of ions in a metal.

The scientist Leon Cooper described that the electon-ion interaction has a secondary effect, a weak interaction between electrons with energies that are close to the Fermi energy. This interaction leads to the formation of weakly bound electronsknown as Copper Pairs.

For most of the superconducting materials a cooper pair has a total angular momentum of zero.

The Bcs theory explained about the supercondutors. It explained about three main properties of the superconductor.

1. Have no resistance below T_c

This is explained by coherence of the superconducting state. Many cooper pairs are in the lowest energy, To lose energy, the entire coherent state would have been broken up and so they required more energy to be supplied on it.

2. Messiner Effect

When a metal is cooled below T_c, no magnetic field can be penetrated a superconductior and also a magnetic field already present in it will also be expelled. On increasing the magnetic field inside a superconductor, the electric field will be induced within the material.

3. Flux Quantization

If a ring of superconducting material is placed into a magnetic field above its critical temperature, the ring lies in a plane perpendicular to the field direction. On lowering the temperature below T_c, it becomes superconducting. The field is expelled either outside the ring or confined within the ring.

The BCS theory implies the magnetic flux through the ring is quantized in units of _o = h/2e.

Where _o is the magnetic flux having the value 2.07*10^-15 Tm² and charge 2e is the charge of a cooper pair.