What are the assumptions of BCS theory?

BSC theory is the first microscopic theory which can successfully explain the properties of superconductivity. The theory was modeled by the efforts of John Bardeen, Leon Cooper and Robert Schrieffer and is commonly called the BCS theory according to the first letter of Bardeen, Cooper and Schrieffer. They received Nobel Prize in 1972 for the development of the theory of superconductivity.

Assumptions of BCS theory:

i) Pairs of conduction electrons in the super conducting state of a solid form bound states.

ii) The force of attraction that binds a pair of electrons arises due to the interaction of electrons with the lattice vibrations (phonons).

iii) The electron pairs can behave like Bosons and can condense into the lowest energy state with zero electrical resistance which is the basis of superconductivity.

The transition of a metal from normal to superconducting state has a nature of condensation of electrons into a lowest energy state. But electrons alone cannot condense into the same energy level (Pauli Exclusion Principle). But according to BCS theory, the electrons close to the Fermi level can couple together to form pair through the interaction with the crystal lattice. Electrons are Fermions, but the pairs of electrons can behave very differently from single electrons. The electrons with anti-parallel spin form the pairs and they are in now bound state with zero spin and zero momentum. Because of having zero spin, electrons pairs can behave like Bosons rather than Fermions and can condense into the lowest energy state (ground state) with zero electrical resistance according to Bose-Einstein condensation. These electrons pairs are commonly known as Cooper Pairs.

The electron pairs have a slightly lower energy and leave an energy gap above them on the order of 0.001 eV which inhibits the kind of collision interactions which lead to ordinary resistivity. For temperature such that the thermal energy is less than the band gap, the material exhibits zero resistivity. The pair condensation is the basis for the BCS theory of superconductivity. This pair formation can be explained through the interaction of electrons with crystal lattice known as electron lattice interaction.