One of the most sought after theories in condensed matter physics is that of high temperature superconductivity. It is hard to walk into these kind of talks and understand what is going on. If it is theory, it’s next to impossible as the first slide almost jumps into a large Hamiltonian, and as I guess these Hamiltonian’s have been discussed ad nauseum by now, people have started to not even describe any of the terms.
In a talk given by Doug Scalapino from the University of California at Santa Barbara, he discussed the question of a pairing ‘glue’ in high temperature superconductors. From what I understand this goes back to last year when Phil Anderson wrote a perspectives in science with the point that if “we have a mammoth and an elephant in our refrigerator - do we care much if there is also a mouse?”
Here the mammoth and the elephant are U, the on site repulsion and J, the exchange interaction in the Hubbard model which describes the transition between conducting and insulating systems. So Anderson says as these interactions are so large why do we need a mouse or a much smaller interaction that is the ‘glue’ that pairs electrons. In ordinary superconducting metals, like lead or Tin, these exchanged particles are phonons (lattice vibrations) that act like a bosonic “glue” to hold the electron pairs together. But what is the ‘glue’ for high temperature superconductors, like the cuprates? Anderson contends that the pairing interaction is coming from J which is instantaneous, attractive and large, so why do we need a smaller interaction to describe the bosonic glue?
Well, the glue that Scalapino was describing was not very clear to me, and it seems that was also the case with some audience members. Indeed, one person did ask at the end of the talk what is the glue and Scalapino’s answer was, well, spin fluctuations. But as Anderson points out these are just a natural consequence of the exchange interaction, J.
I think the jury is still out.