# Monthly Archives: November 2015

## In Favor of Graduate Years in Lab Versus Data-Taking at a Synchrotron

I’m at Cornell High Energy Synchrotron Source (CHESS) this week taking X-ray data, and being here makes me reflect a little on the lab skills I picked up as a graduate student. There are a few reasons for this.

I had tagged along on a couple synchrotron runs in my first year of graduate school and had trouble gaining a conceptual understanding of what was happening during the experiments. For those of you who don’t know, a synchrotron or beam time run is where you go to a X-ray facility to take data, usually for about a week. One usually tries to maximize his/her beam time resulting in very little sleep during these runs. Anyway, part of my conceptual trouble stemmed from the fact that it was difficult for me to understand how the many electronic and X-ray optical components enabled me to take data. For example, how are the X-ray photons hitting the detector turning into the counts on my computer screen?

Despite the fact that I had not been to a beam time run for about five years prior to about a month ago, I somehow now have a much better understanding of the basics of synchrotron-based experiments. I also know exactly why I do as well — it is because I spent those five intervening years toiling away in a lab doing experiments, troubleshooting and picking up some basic laboratory skills.

This made me realize that the graduate years spent in the lab are some of the most important in the development of basic experimental skills. For me, if my experiments had solely required the use of a synchrotron facility, I doubt that I would have picked up many of the basic skills I have today (which can still be vastly improved!). Of course, this is personal and can vary from student to student, but I really do think that time invested in a lab of one’s own pays off in the long term. Synchrotron-based experiments are valuable in that they allow one to take data usually not allowable in the lab. However, for a graduate student to not spend time in a lab — or not to be based at a synchrotron facility if a lot of synchrotron work is needed — may hurt in the long term. This is because synchrotron experiments only last for a week and happen in spurts, while lab work is an everyday activity. Since these beam time runs are so infrequent and an understanding of experiments only happens when one is doing them, an adequate acquisition of basic skills takes longer than it should if one is relying on synchrotron-based experiments.

So if you happen to be starting out as a graduate student and are interested in spectroscopic methods in condensed matter, I think this should be something to consider. Time spent in lab (especially when things don’t work!) does a lot for the development of one’s experimental scientific outlook.

## Excitons in Cuprous Oxide

There is an excellent pair of papers here and here demonstrating the existence of a Rydberg series of excitons in Cu$_2$O, a material that has long been the poster child for observing excitons. The data in both papers are pretty stunning — in the first one, they see a Rydberg series up to n=25! In the second, they see higher angular momentum ($f$-like and $h$-like) excitons apart from the usual $p$-like excitons.

Excitons can occur in semiconductors and insulators and are the result of the Coulomb interaction between electrons and holes. For those familiar with superconductivity, an exciton, in many ways, bears a qualitative resemblance to Cooper pairs, except here the quasi-particles are of opposite charge. Hence, the binding between the electron and hole arises from the usual attractive Coulomb interaction. However, it helps to think of the exciton (similar to Cooper pairs) as possessing a center of mass wavefunction and a relative wavefunction.

The relative wavefunction is then qualitatively and quantitatively similar to the quantum mechanical solution of the hydrogen atom. The main differences are that (1) the reduced mass of the electron-hole pair is usually much less than the reduced mass of the electron-proton system and also that (2) there exists a background dielectric constant, $\epsilon$, that further reduces the energy of the Rydberg series in an insulator. In the simple hydrogen-like picture of the exciton, the energy levels (with center of mass momentum taken to be zero) then have the following energies:

$E_n =- \frac{\mu}{m\epsilon^2}\frac{R}{n^2}$

where $\mu$ is the reduced mass of the electron-hole system, $m$ is the proton mass, and $R$ is the hydrogenic Rydberg.

It turns out that this perfectly spherically symmetric model does not encapsulate completely the exciton in a solid, however, because the potential in a crystal is not perfectly rotation-symmetric. Because of the lattice, the “angular momentum” of the exciton cannot be labeled using an $s, p, d, f$, etc. kind of scheme and we must resort to some group theory.

For the case of Cu$_2$O discussed in the papers above, the symmetry of the crystal is cubic — therefore the symmetry is still relatively high. However, because continuous rotational symmetry is broken, the light used to detect the excitons in this experiment are no longer forbidden from exciting $f$-like and $h$-like excitons and it is remarkable that they are observable!

Even though the observations in these papers can be accounted for in a quite simple theoretical framework, the experimental results are nonetheless quite elegant and remarkable.

As an interesting aside, the reason that this experiment is possible is because of the extreme purity of the Cu$_2$O crystals used for these studies. It turns out the cleanest of these samples are naturally-occurring, rather than man-made.