Thermal conductivity, spinons, and visons

Patrick Lee sent me the following comment on an earlier post on thermal conductivity and visons and asked me to post it.

Ross, I am very glad you brought up the issue of the low temperature thermal conductivity in the ET salt spin liquid. I have been concerned about the data below 0.17 K (T^2 = 0.03) for some time. I think you will find a comparison with the data on the 9 K ET superconductor [Belin, Behnia and Deluzet, PRL 81, 4728 (1998)] amusing.

[This powerpoint slide shows the relevant data, reproduced below, sorry for the small size]

First, because they used different units, the numbers on the y-axis of the superconductor data should be multiplied by 0.1 to compare with the right panel. The point is that the absolute value is very comparable, as pointed out by Mike. More remarkable is that both sets of data show a hump starting below Tc = 9 K for the superconductor and To = 6 K for the spin liquid. The low temperature data shown in the lower panels are also very similar. Behnia stopped his measurement below T = 0.17 K. If we ignore the spin liquid data below the same temperature, one would be tempted to draw a straight line which extrapolates to a finite value of kappa(T)/T = 0.03 W/(K^2m^1), very close to that for the superconductor. To me it is truly amazing that a superconductor and an insulator look so much alike!

What does this all mean? The hump in the superconductor is well understood to have two possible origins. The phonon has a longer mean free path due to the gapping of quasiparticles and the quasiparticles may have increased their contribution to the thermal conductivity due to its longer lifetime. The only way to disentangle them is via thermal Hall measurements. Because the hump looks so much like that of the superconductor, my own inclination is to explore a fermionic spinon explanation before considering “more exotic” objects such as visons. It seems natural to replace the words electron and superconducting by spinon and spinon pairing in the insulator. This has led us to propose a thermal Hall measurement for the insulator (Katsura, Nagaosa and Lee, arXiv: 0904.3227). Yes, the spinons do see an external magnetic field via the spin chirality (or gauge field).

As to the low temperature behavior, I do not understand the experiment well enough to challenge the data. I hope the experiment will be repeated by others. At the same time, it will be useful if Dr. Yamashita will show us data on the superconductor below 0.17 K. This may help answer some of the questions concerning thermal decoupling.