A Review of Theories of Superconductivity

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 Londons' 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 $$T_{\text{c}}$$ . 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. Recently, Christoph Renner through their STM studies observed Caroli–de Gennes–Matricon states (vortex-core states) in YBCO under magnetic field supporting the strong belief that superconductivity in cuprates may be of the BCS type. Li et al., based upon their ARPES data, have proposed a positive feedback mechanism. They argue that the incoherent correlations associated with the strange-metal normal state do not disappear; instead, they convert to strongly renormalized coherent state at temperature well above $$T_{\text{c}}$$ as soon as the superconducting fluctuations set in. More recently, Yanagisawa et al. have proposed that superconductivity in high- $$T_{\text{c}}$$ cuprates is induced by the strong on-site Coulomb interaction. The phase diagrams for 2D Hubbard model and the three-band d-p model show different regions of superconductivity, paramagnetic and ferromagnetic phases. Last word on the theory of high- $$T_{\text{c}}$$ superconductivity is, however, yet to come. MgB2 superconductor discovered in 2001 with $$T_{\text{c}}$$ = 39 K has fortunately turned out to be a BCS superconductor as also supported by the isotope effect. Origin of superconductivity in iron-based superconductors (IBSCs) with $$T_{\text{c}}$$ as high as 55 K and more recently 100 K in a monolayer, discovered in 2008, has proved to be more complicated than the cuprates. Many groups of IBSCs [such as 1111, 111, 11 and 122] with different electronic structures pose problems in finding the right type of pairing mechanism. Newly discovered superconductor, sulphur hydride (H3S) with record $$T_{\text{c}}$$ = 203 K has been found to be a typical BCS superconductor. High $$T_{\text{c}}$$ has been well accounted by the BCS theory with high-frequency optical phonons mediating in pair formation. It appears that the celebrated BCS theory may triumph one day and explain superconductivity in all types of superconductors after taking the peculiar structural parameters into account.