Wednesday, March 15, 2017

The power and limitations of ARPES

The past two decades have seen impressive advances in Angle-Resolved PhotoEmission Spectroscopy (ARPES). This technique has played a particularly important role in elucidating the properties of the cuprates and topological insulators. ARPES allows measurement of the one-electron spectral function, A(k,E) something that can be calculated from quantum many-body theory. Recent advances have included the development of laser-based ARPES, which makes synchrotron time unnecessary.

A recent PRL shows the quality of data that can be achieved.

Orbital-Dependent Band Narrowing Revealed in an Extremely Correlated Hund’s Metal Emerging on the Topmost Layer of Sr2RuO4 
Takeshi Kondo, M. Ochi, M. Nakayama, H. Taniguchi, S. Akebi, K. Kuroda, M. Arita, S. Sakai, H. Namatame, M. Taniguchi, Y. Maeno, R. Arita, and S. Shin

The figure below shows a colour density plot of the intensity [related to A(k,E)] along a particular direction in the Brillouin zone.  The energy resolution is of the order of meV, something that would not have been dreamed of decades ago.
Note how the observed dispersion of the quasi-particles is much smaller than that calculated from DFT, showing how strongly correlated the system is.

The figure below shows how with increasing temperature a quasi-particle peak gradually disappears, showing the smooth crossover from a Fermi liquid to a bad metal, above some coherence temperature.
The main point of the paper is that the authors are able to probe just the topmost layer of the crystal and that the associated electronic structure is more correlated (the bands are narrower and the coherence temperature is lower) than the bulk.
Again it is impressive that one can make this distinction.

But this does highlight a limitation of ARPES, particularly in the past. It is largely a surface probe and so one has to worry about whether one is measuring surface properties that are different from the bulk. This paper shows that those differences can be significant.

The paper also contains DFT+DMFT calculations which are compared to the experimental results.


  1. Two remarks:
    you say (tongue in cheek?) that laser-based ARPES makes synchrotrons unnecessary. I think this is a zero-th order remark, probably based on intensity (flux) arguments. It is incorrect in reality. Laser energies are (mostly) fixed. Most laser based ARPES runs off of Ti-sapphire lasers at 1.5 eV, quadrupled to 6 eV.
    There are some other approaches that go towards 20 eV or higher, but that is not easy, and there are only a few (<5?) instruments in the world that can do that.

    There are multiple reasons that plead for the writing off of synchrotrons due to the presence of lasers, primarily due to the ability to change the photon energy.

    -While it's true that most (electronic...) physics plays out in the first 2 eV or so below Ef (accessible by laser-based ARPES), one has to recognize that having a low photon energy, the accessible section of k-space is also limited.
    This is nice for large-unit-cell materials because of the high k-resolution, but for for a typical lattice constant of ~3-4 A (Si, perovskites), one can barely reach the first zone boundary.
    Not being able to go beyond the zone boundary makes it harder to find some states due to matrix element effects. (Some states are not observed in the first zone, and one has to check farther out.)

    -Being able to change the photon is important for the following reasons:

    -the surface sensitivity depends on the kinetic energy of the emitted electron (which determines its inelastic mean free path). In fact, with 6 eV one is much more bulk sensitive than with a He lamp of 21 eV.
    So your surface sensitivity remark *requires* multiple photon energies to ascertain what one is measuring. With XPS this is done by changing the emission angle, which is possible because core levels don't disperse. ARPES does not have this luxury.
    Moreover, measuring dispersion in z requires scanning the photon energy (due to conservation of only k-parallel). Hence surface states, being intrinsically 2D, can be discriminated from bulk states by changing the photon energy and observing the absence of dispersion with hv.

    -Another argument for the need to be able to change photon energies is that photo-excitation cross sections depend on photon energies. A famous example is the fact that Franz Himpsel figured out that bands made up of dangling bond orbitals on Si surfaces are most efficiently observed by using hv=34 eV. Synchrotrons allow doing this.

    In fact, the authors of this paper found out that 7 eV is mostly surface sensitive *precisely by using synchrotron radiation*.

    The "ARPES is largely a surface probe" remark is (in the context of the surface as the topmost atomic layer - as in the paper) is therefore also incorrect. But indeed, one has to worry about this, and a lot of people don't.
    If one truly wants to know, one should do "normal" ARPES and (hard or soft) X-ray ARPES to compare band structures. See e.g. PRB 94 075141.

    In summary, I think the conclusion you draw about the necessity of synchrotrons is too quickly drawn, and incorrect.

    Other than that, I agree with your post. It highlights how surfaces can be used to study real physics.

    1. Thanks for the expert opinion. I am just a naive theorist. My statement was very poorly written. It should have been something like "for some ARPES experiments it is nice that one does not have to use a synchrotron."

      Synchrotrons are VERY necessary and useful for all sorts of experiments. I would never suggest they are unnecessary.

      I also appreciate you clarifying the surface issue. It is not as simple as I said. The main point is people should talk about this more and theorists should not just blindly believe some ARPES experiment.

      Thanks again for a very helpful comment. I learnt a lot.

  2. typo: "plead against" in the second section.

    (aside: the comment box is only 4 lines tall, which forces one to scroll a lot when reading through a comment before posting - that makes me make mistakes)

  3. Thanks for pointing out the issue with the comments box. I think I just made it wider. You can make the box show more lines using your mouse on the // in the bottom right corner.

  4. Ah yes. So I learnt something too today.

    And I disagree with your statement about being naive. Not knowing something is a reason to ask/learn, not a reason to feel less/naive.

    But now I'm overly critical on every word you write - in the end the fresh views from non-experts can help a lot to sharpen ones own 'expert' view, both when the outside view is correct but even more so when it is not.

  5. Even putting aside the surface sensitivity, it is quite clear that what photoemission measures is NOT simply the single particle spectral function. Noone really knows what photoemission measures. Among other things, different photon energies measure different spectral feature widths. Therefore, its impossible to regard these widths as particle self-energies.

    Whether these are "final state effects" or the inapplicability of the sudden approximation is not clear. This has never been properly addressed in the literature because anyone in a position to address it, has no interest in doing so.

  6. Again I oversimplified things. I agree that ARPES is not a direct measure of the one-electron spectral function because of final state effects and the sudden approximation.