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 liq

uid 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?