What do we really understand about cuprate superconductors?

 At a recent meeting of the condensed matter theory group at UQ we watched the first half of a Harvard (online) seminar that Steve Kivelson gave (at the end of 2020), What do we know about the essential physics of high temperature superconductivity after one third of a century?

As a springboard he takes Phil Anderson's final posting of the arXiv, Last Word's on the Cuprates, from the end of 2016. He was 93 years old then!

Kivelson considers that there are two things we really understand about the cuprates. The first, is that the d-wave superconductivity is intimately connected with the antiferromagnetism of the undoped materials.

The second, is that Tc, the superconducting transition temperature, is determined by thermal disordering of the phase of the order parameter for the superconducting state. This is in contrast to conventional superconductors, where Tc is determined by the amplitude of the order parameter vanishing. 

Kivelson's argument for the first point is based on nice work done a decade ago with Sri Raghu and Doug Scalapino, and that led to other work I have blogged about. It should be stressed that this work is a weak-coupling renormalisation group treatment and so the question remains as to whether the phase diagram for weak-coupling is adiabatically connected to that for strong coupling, which is the regime of the actual cuprate materials. In different works, as U/t increases from very small values to large values there are no phase transitions. Cluster Dynamical Mean-Field Theory (DMFT) studies give some confidence that this is the case. However, not everyone will be convinced by that.

The talk is worth watching, even if at times it gets a bit too technical. It is very important that we have such honest and open reflections about how much progress is (not) being made in a field. I largely agree with Kivelson, but do find the lack of progress rather discouraging and cannot see that this will be inspiring bright young graduate students to enter the field or for funding agencies to put more money into it.