A Review of Theories of Superconductivity

Abstract

The first ever phenomenological theory of superconductivity was propounded by London brothers (Fritz and Heinz) by correlating the current in a superconductor with a vector potential and using Maxwell equations. Theory explained well the vanishing of resistivity and the occurrence of Meissner effect in metallic superconductors. An expression for London penetration depth λ was given which was confirmed experimentally. Another phenomenological theory was proposed by Ginzberg and Landau (G-L theory) introducing the concept of an order parameter and a temperature dependent coherence length which close to 0 K is similar to the temperature independent Pippard coherence length. The most successful theory, the microscopic BCS theory ultimately came from three physicists Bardeen, Cooper and Schrieffer in 1957. They argued that two electrons with equal and opposite momenta form a bound pair (Cooper pair), a boson, via the exchange of a virtual phonon overcoming the Coulomb repulsion. These pairs (bosons) condense into a ground state, a gap appears in the energy spectrum and the system turns superconducting. The energy gap goes down to zero at T _c. Theory however could not explain the so called high temperature cuprate superconductors (HTS) which are similar to BCS superconductors in several respects but differ drastically in many others. There is no evidence of phonon mediation in pair formation in these materials as evidenced from the absence of isotope effect. After many attempts and a long turmoil two theories have found some acceptance. First, is the RVB resonance valence bond (RVB) theory proposed by P.W. Anderson and the other is spin fluctuation theory proposed by P. Monthoux. The two concepts are qualitatively described briefly in this chapter. Last word on theory is, however, yet to come.