Tuesday, May 15, 2007

SCES '07 day 2

Again I only was able to see the morning session today (and will be at Rice until Thursday pm). This means I'll miss the big "BCS@50" plenary session. However, here are a couple of talks that I did get to see....

First, T. Senthil started the day with a talk about spin liquids. This is a theoretically deep concept that I would love to understand better. The basic idea is that one can recast the interacting many-body problem in terms of new excitations of spinons (chargeless spin 1/2 excitations). The cost of doing this is that the spinons have "infinitely nonlocal" statistical correlations. However, these interactions can be made to look simple by introducing some effective gauge "charge" for the spinons and some effective gauge "magnetic field" - then the correlations look like the Aharonov-Bohm effect in this gauge language. If this sounds vague, it's partly because I don't really understand it. The upshot is that the spinons can be fermionic, and therefore have a Fermi surface, and this leads to nontrivial low temperature properties, particularly in systems where the whole weakly interacting quasiparticle picture falls apart. If anyone can point me to a good review article about this, I'd appreciate it.

There were a couple of other strong theory talks. Natan Andrei talked about a general approach to quantum impurities driven out of equilibrium (e.g., as in a quantum dot in the Kondo regime at large source-drain bias). Strong correlations + nonequilibrium is a tough nut to crack. Andrei argued that one can rewrite the problem in terms of scattering of initial states via simple phase shifts, provided that one picks the right (nasty, complicated) basis for the initial states that somehow wraps up the strong correlation effects. This choice of basis is apparently a form of the Bethe Ansatz, which I also need to understand better.

On the experimental side, besides my talk, Gleb Finkelstein from Duke gave a very nice talk about Kondo physics in carbon nanotube quantum dots. The really clever aspect of the work is that, through careful engineering of the contacts to the tube, the actual leads to the dot + the tunnel barriers + the dot itself are all formed out of the same nanotube. As a result the tunnel barriers preserve the special band structure symmetry (SO(4)) of the tube and the leads, leading to profoundly neat effects in transport.


david said...


The question of spinons it's nontrivial. Since the early days of high T_c there have been theoretical arguments that in a strongly correlated insulating system that is an antiferromagnet, under certain conditions when tuned to its paramagnetic phase, such a phase instead of having gapped triplet (spin 1) magnetic excitations, these would fractionalize into spin 1/2 excitations, the putative spinons.

There was a lot of theoretical argument as to what their statitics and their physics would be. It is also true that their nonlocal interactions are equivalent to gauge field interactions for technical reasons which, if you allow me some jargon, amount to a Hubbard-Stratonovih decoupling that acquires dynamics through quantum fluctuations.

In the end, the lack of experimental evidence for spinons
did not allow a resolution of all the questions, and the subject sort of became dormant. Except that theorists sort of concluded that spinons should only exist at critical points between an antiferromagnetic phase and a paramagnetic phase in bipartite 2d lattices or in the paramagnetic phase of a geometrically frustrated 2d lattice. In the first case the spinons would be gapless and in the second case they would be gapped. This view probably has the biggest number of adherents but it is probably less than 50% of the theoretical community. So it is to this day controversial and a large reason it has not been resolved it's the lack of experimental evidence.

Now about a couple of years ago, Kanoda's group in Japan in a organic paramagnetic insulator, measured linear specific heat at very low temperatures. The material is an insulator so there is something spin 1/2 and fermionic that forms a Fermi surface and it is not charged. This lead Patrick Lee and collaborators (somewhat later Senthil and others jumped in the bandwagon)to propose spinons forming a Fermi surface. This ws not envisioned in nay of the previous spinon theoretical studies because even when they were fermionic they were thought to either satisfy a massive or massless Dirac equation and thus not have a Fermi surface.

On the other hand, given the experiment, it is a very reasonable and exciting possibility. Having said this, the material has all sorts of anomalies and not only in the specific heat. There could be other things going on, and the specific heat data is data only a mother could love.

Doug Natelson said...

David - Thanks for your insightful and informative comments. You're right - in fact, Kanoda gave the talk after Senthil, and he showed the linear specific heat data, as well as some other data (Knight shift) that he said could be understood within this picture.

One question I had regarding the linear heat capacity in the organic is the assumption that one does not have to worry about the ubiquitous tunneling two-level systems (TLS). TLS also have an approximately linear in T specific heat at low temperatures. While the crystal quality of the organic is supposed to be extremely high, I have yet to see (in the context of other organics, like pentacene) purities of the sort that would convince me that defects are always negligible.

david said...

Doug, you are correct to be skeptical
that impurities are always negligible. I cannot add anything profound to resolve that issue because it has to be resolved experimentally. If enough further independent evidence (besides the specific heat) accumulates that point to a Fermi surface then one can probably forget about TLS or other things. My take, is that it is an exciting possibility to have a spinon Fermi surface, but it is too early to accept it as real.

The Knight shift is consistent with
a spinon Fermi surface, but this requires somewhat more messy interpretation in my opinion. But, it is true that the Knight shift is
very anomalous once one compares with other paramagnetic insulators and points to very low energy magnetic excitations which can be roughly fitted using a spinon Fermi liquid.

You are right that having a linear specific heat is not enough to conclude there is a Fermi surface, it is only consistent with it and TLS is also consistent with quasi-linear specific heat.

At face value, whether impurities play some role or not in the specific heat, there are plenty of low energy magnetic excitations of an exotic nature. Impurities as far as I know cannot mimic that. Whether it is a spinon Fermi surface or something else requires more exploration.