Friday, June 17, 2011

A primer on unconventional superconductors

For the centenary of the discovery of superconductivity Science has a series of articles about superconductivity. One of the articles is The Challenge of Unconventional Superconductivity by Mike Norman. This a very nice succinct summary of the history, key physics, and open problems. This article will be a particularly good resource for introducing students and new workers to the field. Nevertheless, I also learnt a lot and enjoyed it.

Norman considers the main classes of unconventional superconductors
  • superfluid 3He
  • heavy fermions
  • cuprates
  • organics [at least BEDT-TTF based materials]
  • iron based pnictides
It is great the organics are mentioned and compared to these other materials, since they are often ignored in reviews and conferences on this topic.

I mention just a few important and/or curious things and/or quibbles that come up in the article.

First with regard to superfluid 3He
many factors contribute to the pair interaction, including density, spin, and transverse current interactions (12). Hence, it can be misleading to claim that one mechanism is the sole cause of pairing in unconventional superconductors.
In fact, although more than 30 years have elapsed since the discovery of heavy-fermion superconductors, the actual symmetry of the Cooper pairs of any of them has not yet been unambiguously determined.
[The cuprates] violated most if not all of the empirical search rules set down by Bernd Matthias; these rules were based on the previous record high Tmaterials, which were cubic transition metal alloys, 
[In 1987] a very different theory appeared that, for better or worse, would change the face of physics (34). Philip Anderson, the Nobel laureate, proposed instead that cuprates would exhibit a novel phase of matter where the spins formed a liquid of singlets—the so-called RVB (resonating valence bond) state 
As much as I love RVB theory (and PWA) surely this is overstated! I would not say RVB changed the face of physics. I would just say RVB changed the face of the physics of strongly correlated electron materials.

I don't follow the sentence below about the organics.
These materials were discovered well before the cuprates and were an equal surprise to the community; as Bernd Matthias once quipped, “there aren’t any!” Well, they are indeed real, 
Matthias died in 1980, and the first organic superconductor (TMTSF)2PF6 was discovered in 1979. So I presume this statement [quip?] was made before the discovery and was essentially that he did not believe organic superconductors would ever be found. [Little predicted them with erroneous arguments in 1964. Basically, he ignored the Peierls instability].
[For the iron pnictides] It has been speculated that the order parameter is a so-called s± state, where the Fermi surfaces around the Γ point of the Brillouin zone have an order parameter with one sign, and those around the M point of the zone the opposite sign (46).
I disagree with the use of the word "speculated". Mazin et al. suggested this order parameter based on a concrete RPA calculation using the band structure they obtained from LDA calculations. You can debate whether this calculation is reliable in the parameter regime of the actual materials. Surely, in the weakly coupling limit it is the correct result and involves no free parameters.

Now the punchline:
From a theoretical point of view, it has become increasingly obvious that unconventional superconductivity is a very tough problem. 
Anyway. Great article! Good way to celebrate the centenary. Thanks, Mike. 

1 comment:

  1. Mike Norman sent me the email below and gave me permission to post it.

    Hey, Ross. Well, you know, these article are space constrained, so one can only say so much. For instance, I didn't have space to qualify what I meant about Matthias' comment on organics. It turns out that the statement in question was his reaction to the notice that there would be a conference on organic superconductors. He said he couldn't believe that
    people would actually be holding a conference on materials which didn't exist, and then want on to talk about the harm it would do. Of course, this was indeed 1969, well before the actual discovery, but it was an amusing quote. Another one was about scientists dreaming and reading
    about each other absurdities in a blue haze (like opium addicts), but I didn't have the space to squeeze that one in.

    As for pnictides, what I mean by "speculated" is that there is no proof yet that s+/- is the order parameter. There were weak coupling calculations as well early on in 3He that predicted d-wave, and it turned out to be p-wave, so Mazin or no, I regard it as speculative until we know definitively from experiment.