Deconstructing Homes relation and linear in T resistivity

There is a nice paper
Strong-versus weak-coupling paradigms for cuprate superconductivity
S Asban, M Shay, M Naamneh, T Kirzhner, A Keren

They report very careful measurements of the resistivity versus temperature for four different classes of cuprate superconductors at optimal doping. The goal is to test Homes relation which relates the normal state resistivity to the superfluid density.

Aside: surely it is not appropriate to call this Homes law. Somehow, it does not have the status of Newton's laws or thermodynamics...

In particular, they compare their results to two distinctly different theoretical models that claim to explain Homes relation.

The first model is a conventional "weak-coupling" BCS model for the superconductivity with the resistivity dominated by disorder. One problem with applying this model is that it does not capture the large temperature dependence of the resistivity and that the YBCO materials appear to be particularly clean.

The second model is a hard core boson model, assuming that Cooper pairs still exist well above the superconducting transition temperature. This "strong coupling model" is due to Lindner and Auerbach. In addition to describing Homes relation it also gives a large resistivity, that is linear in temperature, and comparable to the Mott-Ioffe-Regel limit, characteristic of bad metals. One potential problem with this model is that it is only directly relevant to optimally doped curates, whereas the Homes relations seems to hold more or less independently of doping. A major prediction of the model is the relation below, which does not really have any free parameters,

Lambda is the London penetration depth; its inverse square is related to the superfluid density.

The figure below summarises the main results of the paper. The line with q=2 corresponds to the predictions of the above equation.

It is really a matter of personal taste as to whether the above results represent "good" agreement between experiment and theory. As noted in the paper, accurately determining the penetration depth is a tricky business.

The authors also find that, except for YBCO, the resistivity is never really strictly linear in temperature, but only approximately so. This is important because many theorists, particularly the AdS-CFT crowd, assume it is and place great stock on producing a theory with a linear in T resistivity.

There are a couple of things that I like about this paper, compared to your average experimental paper.

First, the authors seem to have been incredibly careful about their measurements. They use different film samples with different thicknesses and different distances between contacts. They check for ohmic behaviour. They see how the resistance varies with "identical" bridges.

Second, the authors compare their results to more than one theory, the goal being to hopefully rule out one of them. This is in the spirit of the method of multiple alternative hypotheses.

I thank Assa Auerbach bringing this paper to my attention. He comments on it via my earlier post on his work on the hard-core boson model.