A qualitative discussion of a successful theory of superconductivity was given by Bardeen, Copper and Schrieffer, known as BCS theory after the initials of their names. This theory accounts for all properties of superconductors.
(a) Electron –phonon Interaction. BCS theory showed that the basic interaction responsible for superconductivity appears to be that of a pair of electrons by means of an interchange of virtual phonons. This is explained as follows:-
Suppose an electron approaches a positive ion core. It suffers attractive coulomb interaction. Due to this attraction ion core is set in motion and thus distorts that lattice. Let a second electron come in the way of distorted lattice and interaction between the two occurs which lowers the energy of the second electron. The two electrons therefore interact indirectly, via lattice distortion or the phonon field, thus lowering the energy of electrons. This type of interaction is called electron-lattice is quantized in terms of phonons the above interaction can also be interpreted as electron –electron interaction through phonons.
Let an electron of wave vector K emits phonon q, which is absorbed by an electron of wave number K .K is thus scattered as K-q and K as K –q the process being a virtual one. The nature of the resulting electron-electron interactions depends on the relative magnitudes of the electronic energy change and the phonon energy. If this phonon energy exceeds electronic energy, the interaction is attractive.
(b) Copper Pairs. The fundamental postulate of BCS theory is that the superconductivity occurs when an attractive interaction mentioned above, between two electrons by means of a phonon exchange, dominate the usual repulsive coulomb interaction. Two such electrons which interact attractively in the phonon field are called copper pair.
(c) Coherence length. The paired electrons are not scattered and can maintain their coupled motion up to certain distance called the coherence length. It is a measure of the distance within which the gap parameter does not change very much in varying magnetic field.