The understanding of superconductivity was advanced in 1957 by three American physicists-John Bardeen, Leon Cooper, and John Schrieffer, through their Theories of Superconductivity, know as the BCS theory.
The BCS Theory deals with the behaviour of electrons in superconducting materials at very low temperatures.
Statement
It states that an electron pair called cooper pair is formed at low temperature by overcoming the repulsive force. The cooper pair moves without scattering (without any resistance) in the lattice structure. Now the material becomes a super conductor.
The distance up to which two electrons combine to form a Cooper pair is Called Coherence length
This is also called as electron-phonon-electron interaction. These two electrons have equal and opposite momentum and spins. This BCS theory is suitable only for low temperature superconductors.
The BCS theory successfully shows that two electrons can be attracted through interactions with the crystalline lattice. When electrons are linked together in pairs, they move through the superconductor in an orderly fashion.
Normally, the electrons repel each other and are scattered by the lattice, creating resistance. Due to this, lattice vibrations are produced, and the atoms are in a compressed state (Distortion), so it will create a high positive ion region. Now a second electron passing is attracted towards this positive region and in a superconductor it follows the first electron and they travel bond together through the lattice.
Explanation
An electron moving through the material at low temperature, encounters less resistance due to vibrational distortions of the lattice. The Coulomb attraction between the passing electron and the positive ion distorts the crystal structure.
The region of increased positive charge density propagates through the crystal as a quantized sound wave called a phonon. The passing electron has emitted a phonon.
Fig 1.1: Crystal lattice distortion
A second electron experiences a Coulomb attraction from the increased region of positive charge density created by the first electron. Electrons are said to pair into Cooper pairs through interaction with the crystal lattice. Cooper pairs are formed by two electrons, which overcome their Coulomb repulsion and experience an attraction through phonon exchanges. Cooper Electron Pairs act like single particles (BOSONS). The electrons in a Cooper Pair possess anti-parallel spin, resulting in a total spin of zero for the pair.
Fig 1.2 : Formation of cooper pair
Cooper pairs condense into a highly ordered ground state. The pairs retain this ordered structure while moving through the crystal lattice. Each pair becomes locked into its position with others pairs, and as a result no random scattering of electron pairs may occur.
Zero resistivity may be defined as the absence of electron scattering; hence, the superconductor now demonstrates zero resistivity.
The binding energy of a Cooper pair at absolute zero is about 3KTc. As the temperature rises the binding energy is reduced and goes to zero when T=Tc. Above Tc the Cooper pair is not bound.
BCS theory predicts the following
- Isotope effect,
- Variation of critical field with temperature.
- Existence of energy gap between the ground state [Superconducting state] and the first excited state.
- Quantization of the magnetic flux in a superconductor ring.
RVB Theory (Resonance Valence Bond Theory)
It is Applicable for high temperature superconductor. It is based on the idea that the short range repulsive force between the electrons in a narrow band. Superconductivity occurs when the material is doped to create holes in it. These holes then form pairs and undergo Bose condensation.
| Read More Topics |
| Hard and soft magnetic material |
| Charge densities in a semiconductor |
| Electrical conductivity in intrinsic semiconductor |
