Superconductivity and high‐Tc superconductors
Authors: Cyrot M. 
Published: May 2022

Although discovered in 1911, it was only in 1956 that superconductivity was explained by Bardeen, Cooper and Schrieffer. The superconducting state is an example of macroscopic quantum state. The basic idea is that, due to an attraction between electrons through exchange of phonons, electrons pair. Superconductivity is thus described by a quantum mechanical amplitude for finding electrons in a paired state. High temperature superconductivity was discovered in 1986 by Bednorz and Müller in cuprates. However, contrary to all expectations, it still awaits an explanation which has a general a consensus.

This situation is due to a number of basic experimental facts which are rather unusual but on which a consensus has grown since the discovery. We list them:

• An unusual phase diagram. The two important points are that the undoped material is a Mott insulator (i.e., not a band insulator) and a strange high temperature metallic phase appears.

• The superconducting cuprates are very high kappa materials due to an extremely small coherence length compared to low‐temperature materials and a large pentration depth.

• Most experiments tend to prove that, contrary to conventional materials, cuprates are d‐wave superconductors.

• Many properties of the superconducting state remain unclear as the explanation is concerned. For example the scattering by impurities, Uemura's plot etc.

The normal state of these materials is also very unconventional compared to usual metals. The most interesting property is the existence of a pseudogap below a temperature T* in the underdoped materials. This is directly observed in experiments as ARPES or tunnelling and it explains the unconventional behavior of many other physical properties.

BCS theory starts from a normal state which is a Fermi liquid. Due to the anomalous properties of the normal state, the first basic question is: Is the normal state of the superconducting cuprates a Fermi liquid or not? ARPES measurements tend to answer that question. However although the improvement of this technique has been considerable and the results are of valuable interest, this has not given a completely satisfactory answer to this question. The lifetime of the excitations is not Fermi‐liquid like although some explanations exist for that result, and some authors believe that quasiparticles exist only in the superconducting state. The results obtained on the pseudogap are very significant and show how it appears with decreasing temperatur below T*.

This raises the problem of the origin of the pseudogap. Two opposite explanations have been proposed. A magnetic origin, i.e., either magnetic fluctuations, which have been observed in the underdoped materials, or spin density waves or now fluctuating stripes. This origin permits to explain some of the properties but it remains unclear why the conductivity increases with the appearance of the pseudogap in this scenario.

Alternatively, the origin is linked to superconductivity. Fluctuations in the normal state are always believed to be reduced to a small rang of temperatures even in the case of cuprates where the extremely small coherence length permits a considerably larger range than in conventional superconductors. However simple considerations from the Ginzburg criterion show that the mean‐field BCS temperature can be reduced by an important factor in the extrem type two superconductors and in that case would correspond to T*. The real Tc would obey Uemura's plot. This scenario explains also a lot of unconventional behaviors but would imply that the pseudogap develops continuously into the superconducting gap. However, this is a subject of controversy.

Above‐T* magnetic fluctuations could explain the anomalous behavior of various quantities (life time of quasiparticles, resistivity, hall effect etc.) but others explanations exist.

Various physical origins for the pairing have been proposed. We list and comment some of them.

• Conventional superconductivity

High temperature superconductivity would be explained by van Hove singularities. This scenario has little support due to the fact that too many properties suggest large correlations effects.

• Spin‐charge separation

The elementary excitations would not be quasiparticles but fractionalized electrons, on part carries the spin quantum number and the other the charge. Different versions of superconductivity based on this idea have been first proposed by Anderson. However, spin‐charge separation is known to occur in one dimension. When and if it occurs in two dimensions is a subject of current controversy.

• Fluctuating stripes

They could be the reason of spin charge separation. However, nobody knows the role of fluctuating stripes in superconductivity. They may be crucial or harmful.

• Spin‐fluctuation mechanism

First proposed by Scalapino, there exist now a great number of detailed calculations due to Pines and coworkers and Moriya et al. using his self‐consistent renormalized theory. They give good agreement with experiments. However, a basic objection has been put forward by Schrieffer: Why does one not observe superconductivity frequently around the antiferromagnetism instability?

• Other mechanisms

They are too numerous to be discussed. However as there is quasi consensus that superconductivity occurs in between a Mott insulator and a usual metal, on must seriously consider the way of disappearance of the Mott state by doping. With doping, this provides a lower Hubbard band of quasilocalized states and a band of itinerant states. This permits a scenario where superconductivity appears in the itinerant band due to collective excitations in the quasilocalized band. Following this line one can consider excitons and propose an excitonic scenario.

Although high‐Tc superconductivity has provided a lot of new theoretical ideas, we suspect that the broader area of strongly interacting quantum systems will be an active field of research during the next years and the full understanding of the doped Mott insulator will permit a consensus about high‐Tc superconductivity.