Wednesday, April 1, 2015

What does it mean to "observe" a Fermi surface?

The primary point of this post is to raise a philosophical question, "What is definitive experimental evidence for the existence of quasi-particles and a Fermi surface in a metal?"
Specifically, if one sees quantum oscillations, such as Shubnikov de Haas, or maps out the Fermi surface using Angle Dependent MagnetoResistance, has one "seen" the Fermi surface?

The secondary point is an unfortunate one. It provides another concrete example of the perverse influence of luxury journals, particularly the Nature Publishing Group, on science.
People make silly unjustified claims to get published.

At first I was excited when I saw the Nature Communications paper
Quasiparticles and Fermi liquid behaviour in an organic metal 
 T. Kiss, A. Chainani, H.M. Yamamoto, T. Miyazaki, T. Akimoto, T. Shimojima, K. Ishizaka, S. Watanabe, C.-T. Chen, A. Fukaya, R. Kato, S. Shin

It reports Angle Resolved PhotoEmission Spectroscopy (ARPES) measurements on an organic metal. For the last 20 years ARPES has been a workhorse for studying cuprate superconductors. However, organics seem to have been beyond its reach, partly because the crystals can be easily damaged by the high intensity X-rays used. When I give talks about organics people often ask about ARPES measurements. So, I thought perhaps finally the time had come.
The authors of the paper are to be commended for taking on this challenging task.

The abstract of the paper states

Many organic metals display exotic properties such as superconductivity, spin-charge separation and so on and have been described as quasi-one-dimensional Luttinger liquids. However, a genuine Fermi liquid behaviour with quasiparticles and Fermi surfaces have not been reported to date for any organic metal. Here, we report the experimental Fermi surface and band structure of an organic metal (BEDT-TTF)3Br(pBIB) obtained using angle-resolved photoelectron spectroscopy, and show its consistency with first-principles band structure calculations. Our results reveal a quasiparticle renormalization at low energy scales (effective mass m*=1.9 me) and ω2 dependence of the imaginary part of the self energy, limited by a kink at ~50 meV arising from coupling to molecular vibrations. The study unambiguously proves that (BEDT-TTF)3Br(pBIB) is a quasi-2D organic Fermi liquid with a Fermi surface consistent with Shubnikov-de Haas results.

Then I looked at the actual data in the paper. Some is shown below.
It is rather noisy!
The lower figure shows the deduced Fermi surface on top of an ARPES intensity map.

Based on the quality of the data, I don't think it is appropriate to state "The study unambiguously proves that (BEDT-TTF)3Br(pBIB) is a quasi-2D organic Fermi liquid with a Fermi surface".

What do you think?

Prior to this paper there were Shubnikov de Haas measurements on the same material and Angle-Dependent MagnetoResistance, reported here. The data is shown below.

This is clean and impressive. Indeed the beating in the SdH and the peaks in ADMR at 90 degrees reflect that there is actually a coherent three-dimensional Fermi surface, a warped cylinder.

From the ADMR one can map out the intra-layer Fermi surface, using some theory, which assumes Fermi liquid quasi-particles. The result is below. The area is consistent with the frequency of SdH oscillations.

The authors neglect to mention this, even though they reference the paper that contains this figure. Furthermore, they make the extraordinary claim,

the present result constitutes the only case of an experimentally measured k-resolved Fermi surface of an organic metal. 

I am gobsmacked because in 1996 a book was published
Fermi Surfaces of Low-Dimensional Organic Metals and Superconductors by Joachim Wosnitza.
It contains multiple pictures of "experimentally measured k-resolved Fermi surfaces".

If you asked me "Does this material have a Fermi surface?" I would say, purely based on the ADMR that I was pretty confident it did.

Putting aside all the noisy data and hype, there is an important philosophical and scientific question,
"Is ARPES really a more fundamental measurement of or robust evidence for a Fermi surface than ADMR and SdH?"
There are some subtle issues here, as discussed here. For example, with a marginal Fermi liquid one can still get SdH.


  1. The Fermi edge they measure (along one direction in k-space) appears real; the Fermi distribution fit matches. But I presume this has been measured and published before.

    Their Fermi surface can not be qualified as such because they omit to note in which energy range these data were integrated.
    This matters because ideally one would want to measure "at" the Fermi surface, meaning integrating in an energy range equating the measurement temperature. For their measurement at 4 K that equates to 1/3 of a meV.
    That is not possible (not enough counts), so they integrated over a larger energy range. That should have been mentioned in the paper.

    So, to back up their claim of a Fermi surface, they should have provided EDCs (intensity versus energy) with Fermi edges along (many) more directions. Fitting Fermi edges to all of these would make their claim quite plausible.

    Regarding the transport approach to measuring Fermi surfaces - I think the ARPES approach suffers from similar issues as illustrated above. A marginal Fermi liquid could still give the appearance of a Fermi surface when the 2D plot as a fct of kx and ky is integrated over an energy range that is too large.

  2. I agree with pcs... There are many NFLs that in principle could masquerade as FLs (and vice versa Ex. see below) in an ARPES experiment because of finite energy resolution and other things. To distinguish a FL, one needs to resolve a discontinuity in the momentum occupation function n(k) as T->0. That of course is not possible from an experimental perspective and so then the question is what is the best criteria to resolve a discontinuity manifesting itself gradually at low T. I don't have a good answer for that and I don't believe anyone does. The experiment Ross highlights obviously doesn't meet any rigorous standards in that regard and the conclusions are overblown.

    It is important to keep in mind a few other points with regards to what photoemission measures. First it is far from clear that ARPES measures precisely the single particle spectral function of the bulk material. That it does, requires first that the surface electronic structure reflects the bulk. But more fundamentally it also requires that the "sudden approximation" be valid. This is the approximation that the photoelectron leaves the solid instantaneously such that the material cannot relax. It is clear that in many good ARPES experiments, the data reflects "something like" the single particle spectral function. The phenomenology is too self-consistent for it to be something else entirely, but I would point out that ARPES linewidths are always much much larger than one would expect them to be from transport etc. This could be the different nature of momentum relaxation vs. quasiparticle relaxation, but I suspect that that is not the whole story.

    So what is a more robust measure of a Fermi surface? In general I would say the transport probes are more robust, because they have essentially infinitely good energy resolution (for the examples cited) and its clear what quantity is being measured. But I would also point out there are systems like the nu=1/2 FQH state, that show quantum oscillations, but are believed to be NFLs. In the nu=1/2 FQH case even the Lifshitz-Kosevich formalism seems to make sense with parameters roughly expected for the composite fermions. So perhaps we have to evaluate things on a case by case basis.

  3. Peter makes a few good points, in particular w.r.t. the surface electronic structure (do hv dependent ARPES, if the states don't disperse in kz, they could be surface states instead of bulk, although for layered weakly coupled materials that is a bit hard to figure out).

    I would like to add that we know that the sudden approximation is not valid; hence multiplet splitting in core levels of elements with magnetic moments in their valence band (the up/down core hole created in the PES process couples to the moment, creating two peaks at different energies - see e.g. interesting recent work on the pnictides - this means that what is measured is the state where the hole is already present, i.e. the system has relaxed).

    I agree though it is in a first approximation a good starting point to look at the single particle spectral function (similar as "start with LDA"). But once going into the physics, one should be very careful to know the limitations of that approach, even if the final detailed correct model is not known.

  4. Hi pcs and Peter,

    Thanks for these very helpful and insightful comments. Your ARPES expertise is much appreciated.
    Your comments underscore and support my two main points.

    1. There is some very interesting and subtle physics here.

    2. The authors, referees, and Nature PG editors have done a very poor job. Again hype has trumped careful science and scholarship.