Monday, May 4, 2009

Dimensionless ratios for metals III: Lorenz

In metals at low temperatures both the electrical conductivity and thermal conductivity are dominated by their contributions from electronic motion. Furthermore, it is possible to form a ratio (the Lorenz ratio) of the two conductivities which only depends on fundamental constants (Boltzmann's constant and the charge on an electron) and the temperature. This is known as the Weidemann-Franz law after the two physicists who discovered an empirical version of the law in 1854. The law has turned out to be incredibly robust, holding at low temperatures, for every known metal, including strongly correlated electron materials. Theoretically the law is a consequence of the existence of quasi-particles and Fermi liquid theory. Image copyright

However, experimental results on a heavy fermion material, published in Science in 2007, suggested that near a quantum critical point, the law was violated for interlayer currents. Piers Coleman wrote a provocative commentary discussing how this showed the destruction of quasi-particles near the quantum critical point.

Recently, Michael Smith at UQ did detailed calculations to see if the experimental data can be quantitatively described in terms of a standard Fermi liquid model in which antiferromagnetic spin fluctuations, which diverge at the quantum critical point. It turns out that they can. In a PRL, we show that the WF law still holds, but the temperature scale below which it does vanishes as the quantum critical point is approached. Furthermore, the apparent violation seen by the experimentalists was a result of extrapolating experimental data from 25 mK to 10 K down to zero temperature. It turns out one will need to go to even lower temperatures to see recovery of the Weidemann-Franz law.

One question I have relates to a question raised at the end of a previous post. Deviations from the Kadowaki-Woods ratio were used to characterise the breakup of heavy electrons near a quantum critical point.
Is it possible that the apparent violation of the universal value for the Kadowaki-Woods ratio near the quantum phase transition is also an artefact of the relevant coherent temparature, below which Fermi liquid behaviour occurs, being lower than that of the experiment?


  1. Ross:

    Great idea to start a Condensed Matter Blog. I've haven't had chance to read your paper with Michael Smith. It has many elements in common with the old work of Paul and Kotliar, and I was surprised that you did not reference this work!

    I have many issues with the "2D" spin fluid idea. But my main objection - is simply - why should we expect the spin fluid to be 2D in intermetallic systems that are in essence, three dimensional? Indeed - the recent measurements by the Los Alamos group show that near the QCP of the closely related CeRhIn5, the transport anisotropies become smaller, rather than larger.
    Even in frustrated systems, one expects a cross-over to 3D behaviour at low T. Any reasonable estimate of such cross-over scales would be unable to account for the 200:1 resistance ratio over the full range of the linear resistivity.

    My more serious concern however, is the growing
    suspicion that we are not just dealing with a quantum critical point, but that there are strong experimental signs of a strange metal phase between the Fermi liquid and the antiferromagnet. Indications to this effect are present in YRS (doped with Ge and with Ir), and in YbAlB4.

    Well. Thats a quick comment to get things going.

    But a very interesting paper and I look forward to more discussion.

  2. Piers,

    Thanks for the interest,

    I agree that the case for the two-dimensionality at milliKelvin T is questionable.

    One response I would make is that the WF violation in CeCoIn5 was reported only for very low T, at fields close to the 5T QCP, and only with current perpendicular to the conducting layers. On the other hand, T-linear resistivity is seen over a wide temperature and field range and for current in either direction (at least above a few Kelvin).

    So, one could argue that inelastic scattering from 2D spin fluctuations could make an important low-T contribution to deviations from the WF law--and examine this effect without tackling the problem of the far-more-robust T-linear resistivity. The fact that a naive calculation using a 2D SDW picture accounts very well for the characteristic temperature and field dependence of deviations from the WF law gives some justification for this after the fact.

    If WF violation can be thus explained then one can re-examine transport phenomena over larger T scales using models in which quasiparticles remain intact.