# Monthly Archives: November 2015

## Misconduct and The Wire

Season five of the critically acclaimed TV show The Wire tackles the issue of journalistic fraud and misconduct. In particular, Scott Templeton, a young ambitious journalist at the Baltimore Sun, writes a series of articles where he embellishes details, conjures up quotes out of thin air and ultimately fabricates events. His articles win him wide praise among those in the journalism community. He also garners the Pulitzer Prize, one of the highest accolades one can earn in the field. Even though flags are raised by some of his peers at the Baltimore Sun, at the upper management level, Scott Templeton’s stories are celebrated with enthusiasm.

Of course The Wire is fictional, but at the time The Wire was written, there was precedent for such journalistic falsification. Stephen Glass at the New Republic, Janet Cooke at the Washington Post and Jayson Blair at the New York Times had all been found guilty of journalistic misconduct associated with either plagiarism or fabrication in effort to advance their careers. Cooke was even awarded a Pulitzer Prize for her stories, which she eventually returned.

The reason I bring this all up is because I saw a very strong parallel between the fictional events that occurred in The Wire surrounding Scott Templeton and the actual events that occurred with respect to Jan-Hendrik Schon. In both cases, their notebooks were empty, there were claims by both that their information (e.g. data and notes) had somehow been corrupted and their sources were a closely guarded secret. While working at Bell Labs, Schon famously claimed to use the evaporator in Konstanz, Germany, so that he could “work” in isolation, making it more difficult to for others to reproduce his methods.

The question as to why this kind of misconduct takes place is an interesting one. In the case of Jayson Blair, Wikipedia says:

On the NPR radio show Talk of the Nation, Blair explained that his fabrications started with what he thought was a relatively innocent infraction: using a quote from a press conference which he had missed. He described a gradual process whereby his ethical violations became worse and contended that his main motivation was a fear of not living up to the expectations that he and others had for his career.

As can be gleaned from the quote above, there is little doubt that there is a certain amount of careerism and elevated expectation that is tied in with these instances of misconduct. That these and similar cases occur with relative frequency and happen in different fields suggests that the root cause is societal — an emphasis on perceived career success rather than valuing honesty and hard work. Because this is a sociological problem, all of us have a role to play in correcting it. The solution to the problem may require us to emphasize different values: integrity, meaningfulness of labor and honest motivations. Often these are not the qualities that advance one’s career, but this is because of a lack of emphasis on these values. Perhaps they should.

While the Wire is a fictional show and some readers are no doubt a little fed up with my frequent references to it, I do think that one can learn a lot from its main themes. As Tim O’Brien, author of The Things They Carried, said:

That’s what fiction is for. It’s for getting at the truth when the truth isn’t sufficient for the truth.

## Neutron Scattering and Cuprates

Because many of us were born after the cuprates were discovered, and because of the sheer number of papers that have been written on them, it can seem like a daunting task for the young researcher to get a good grip on high-temperature superconductivity. Fortunately, there are some great review papers out there that help synthesize a lot of data and provide references to much of the original work. These review articles tend to concentrate either on one experimental technique or one part of the cuprate phase diagram (e.g. the pseudogap).

In a similar spirit, this blog post will concentrate on some of the significant findings in the cuprates discovered using neutron scattering. It should be kept in mind that most neutron scattering experiments have been done on YBCO and LSCO because large single crystals can be made of these compounds. The list below is a little biased, but I hope some will find it useful.

1. Spin Gap: A low energy gap in the magnetic inelastic neutron scattering  cross section has been observed  below Tc in both optimally doped LSCO and YBCO. For YBCO, the magnitude of the spin gap is larger (consistent with its higher Tc) and the spin gap exists for underdoped and overdoped samples as well. In YBCO the relation $2\Delta_s=3.8k_BT_c$ is approximately observed, where $\Delta_s$ is the magnitude of the spin gap.
2. Dispersive Incommensurate Fluctuations and the Hourglass Spectrum: There exist incommensurate magnetic fluctuations near the antiferromagnetic Bragg point in both underdoped and optimally doped LSCO and YBCO. These peaks show up in the magnetic inelastic neutron scattering cross section and seem to gain in intensity below the superconducting transition. On a $\delta$ vs. energy plot (where $\delta$ is the incommensurability away from the anti-ferromagnetic Bragg point) the spectrum seem to have an hourglass-like shape. It should be noted that (to my knowledge) the hourglass spectrum has not been observed in electron-doped cuprates with studies having been conducted on (NCCO and PLCCO).
3. Resonance Mode: The magnetic resonance mode is a peak at ~40-50meV, which is located at the “pinching point” in the hourglass spectrum. This peak has been observed in many underdoped and optimally doped cuprates, including BSCCO and TBCCO. It is probably the weakest in  LSCO, where it is broad and does not carry much spectral weight. It also only shows up dramatically around Tc. Interestingly, a similar mode has been seen in electron-doped cuprates and some of the Fe-based superconductors.

While there have been some other discoveries in the cuprates with neutron scattering, most of the studies tend to concentrate on one or all of these three general experimental observations.

Here are some links to some papers which discuss these observations in a little more detail:

## Hunches and Feelings

In speaking with other physicists, I have noticed that some of the most productive avenues to go down is to share feelings and hunches about a particular phenomenon. These intuitions are not usually written down anywhere because sometimes they are pure speculation. Therefore, it is important to talk, share and be open to suggestions from others.

Once in a while, there are opinion pieces in journals that are quite interesting to read where physicists do share these very speculations. Here is one example of this from Nature Physics where some prominent theorists working on high-temperature superconductivity have shared some ideas. I have to say that reading this piece gave me a couple ideas for experiments — and these are the kinds of articles that are the most likely to do so. This article is 10 years old, however, and some ideas may be a little dated.

Nevertheless, it is unfortunate that articles like these are not very common, even though they can be of immense value. I think this is a format that journals should pursue more widely, and I urge them to seek out pieces like these in the future.

Comments and opinions regarding this issue are encouraged.

## Balibar and his Beef with Science Magazine’s Depiction of a BEC

I’m coming to the end of reading Sebastian Balibar’s physics book (intended for a general audience) entitled The Atom and the Apple. Thematically, the book works by asking a basic question at the beginning of each chapter and seeing the wondrous science that has to be understood to answer such a basic question. The author pulls on a dangling thread and watches entire garments unravel. The book is interspersed with personal anecdotes, which gives the physics some semblance of humanity.

Just to whet your appetite a little, let me recount one of the amusing stories Balibar relays. In 1995, following the discovery of Bose-Einstein Condensation by the Colorado and MIT groups, Science had the following image on the cover (sorry, I couldn’t find a large picture in color anywhere, it’s supposed to be primarily blue if that helps). It shows marching soldiers, a supposed metaphor for BEC.

Balibar takes issue with this representation and goes onto say about the cover:

No, what bothered me was actually that march—those orderly
troops. True, I had bad memories of my own experiences with military marches. Before May 1968, the hierarchy at the École Polytechnique had little patience for the antics of its rebel students, and my deviance had cost me fifteen days in prison and gotten me barred from marching with my fellow students on the Champs Élysées. But regardless of these youthful memories, I saw in that march of atoms a basic error of interpretation as to what the recently discovered “Bose-Einstein” condensation was. The order of the actual condensate seemed radically different to me from the regimentation depicted on the magazine cover.
The artist at Science hadn’t just dreamt up this march all by him or herself, though: the military analogy had been hanging around in the public scientific discourse for a long time. Nevertheless, in becoming famous, this image threatened to distort the understanding of the discovery. I intended to denounce it firmly.

What Balibar had in mind about BEC is much more accurately depicted in this great little video.

The book also has some anecdotes about the history and controversy surrounding the Nobel Prizes awarded for superfluidity in liquid helium-4 among many other interesting historical detours. The discussion on radioactivity is also noteworthy. This charming little book is written with an approach that I feel more popular physics books should take, or Balibar could write a couple more himself.

## Plasma Frequency, Screening Response Time and the Independent Electron Approximation

The plasma frequency in the study of solids arises in many different contexts. One of the most illuminating ways to look at the plasma frequency is as a measure of the screening response time in solids. I’ve discussed this previously in reference to the screening of longitudinal phonons in semiconductors, but I think it is worth repeating and expanding upon.

What I mean by “screening response time” is that in any solid, when one applies a perturbing electric field, the electrons take a certain amount of time to screen this field. This time can usually be estimated by using the relation:

$t_p = \frac{2\pi}{\omega_p}$

Now, suppose I introduce a time-varying electric field perturbation into the solid that has angular frequency $\omega$. The question then arises, will the electrons in the solid be able to respond fast enough to be able to screen this field? Well, for frequencies $\omega < \omega_p,$ the corresponding perturbation variation time is $t = 2\pi/\omega > t_p$. This means the the perturbation variation time is longer than the time it takes for the electrons in the solid to screen the perturbation. So the electrons have no problem screening this field. However, if $\omega > \omega_p$ and $t < t_p$, the electronic plasma in the solid will not have enough time to screen out the time-varying electric field.

This screening time interpretation of the plasma frequency is what leads to what is called the plasma edge in the reflectivity spectra in solids. Seen below is the reflectivity spectrum for aluminum (taken from Mark Fox’s book Optical Properties of Solids):

One can see that below the plasma edge at ~15eV, the reflectivity is almost perfect, resulting in the shiny and reflective quality of aluminum metal in the visible range. However, above $\hbar\omega$=15eV, the reflectivity suddenly drops and light is able to pass through the solid virtually unimpeded as the electrons can no longer respond to the quickly varying electric field.

Now that one can see the effect of the screening time on an external electric field such as light, the question naturally arises as to how the electrons screen the electric field generated from other electrons in the solid. It turns out that much of what I have discussed above also works for the electrons in the solid self-consistently. Therefore, it turns out that the electrons near the Fermi energy also have their electric fields, by and large, screened out in a similar manner. The distance over which the electric field falls by $1/e$ is usually called the Thomas-Fermi screening length, which for most metals is about half a Bohr radius. That the Thomas-Fermi approximation works well is because one effectively assumes that $\omega_p \rightarrow \infty$, which is not a bad approximation for the low-energy effects in solids considering that the plasma frequency is often 10s of eV.

Ultimately, the fact that the low-energy electrons near the Fermi energy are well-screened by other electrons self-consistently permits one to use the independent electron approximation — the foundation upon which band theory is built. Therefore, in many instances that the independent electron approximation is used to describe physical phenomena in solids, it should be kept in mind the hidden role the plasmon actually plays in allowing these ideas to work.

Naively, from my discussion above, it would seem like the independent electron approximation would then break down in a band insulator. However, this is not necessarily so. There are two things to note in this regard: (i) there exists an “interband plasmon” at high energies that plays essentially the same role that a free-carrier plasmon does in a metal for energies $E_g << E < \hbar\omega_p$ and (ii) whether the kinetic or Coulomb energy dominates will determine the low energy phenomenology. An image below is taken from this paper on lithium fluoride, which is a band insulator with a band gap of about 5eV and exhibits a plasmon at ~22eV:

The interband plasmon ultimately contributes to the background dielectric function, $\epsilon$, which reduces the Coulomb energy between the electrons in the form:

$V_{eff} = \frac{e^2}{\epsilon_0 \epsilon r}$

For example, this is the Coulomb interaction felt between an electron and hole when an exciton is formed (with opposite sign), as can be seen for LiF in the above image.

Now, the kinetic energy can be approximated by the band width, $W$, which effectively gives the amount of “wavefunction overlap” between the neighboring orbitals. Now, if $W >> V_{eff}$, then the independent electron approximation remains a good approximation. In this limit, one can get a band insulator, that is adequately described using the independent electron approximation. In the opposite limit, however, often one gets what is called a Mott insulator. Because d- and f-electrons tend to be closely bound to the atomic site, there is usually less wavefunction overlap between the electrons, leading to a small band width. This is why Mott insulators tend to occur in materials that have d- and f-electrons near the Fermi energy

Most studies on strongly correlated electron systems tend to concentrate on low-energy phenomenology.  While this is no doubt important, in light of this post, I think it may be worth looking up from time to time as well.

## Why Was BCS So Important?

BCS theory, which provides a microscopic framework to understand superconductivity, made us realize that a phenomenon similar to Bose-Einstein condensation was possible for fermions. This is far from a trivial statement, though we sometimes think of it as so in present times.

A cartoon-y scheme to understand it is in the following way. We know that if you put a few fermions together, you can get a boson, such as 4-helium. It was also known well before BCS theory, that one gets a phenomenon reminiscent of Bose-Einstein condensation, known as superfluidity, in 4-helium below 2.17K. The view of 4-helium as a Bose-Einstein condensate (BEC) was advocated strongly by Fritz London, who was perhaps the first to think of it in such a way.

Now let us think of another type of boson, a diatomic molecule, as seen in gas form below:

Even if the individual atoms were fermions, one would then predict that if this bosonic diatomic gas molecule could remain in the gas phase all the way down to low temperature, that at some point, this diatomic gas would condense into a BEC. This idea is correct and this is indeed what is observed.

However, the idea of a BEC becomes a little more cloudy when one considers a less dilute diatomic gas where the atoms are not so strongly bound together. In that case, the cartoon starts to look something like this:
Here the “diatomic molecules” are overlapping, and it is not easy to see which atoms are paired together to form the diatomic molecule, if one can even ascribe this trait to them. In this case, it is no longer simple to see whether or not BEC will occur and indeed if there is a limit in distance between the molecules that will necessarily give rise to BEC.

This is the question that BCS theory so profoundly addresses. It says that the “diatomic molecules” or Cooper pairs can span a great distance. In superconducting aluminum, this distance is ~16,000 Angstroms, which means the Cooper pairs are wildly overlapping. In fact, in this limit, the Cooper pair is no longer strictly even a boson, in the sense that Cooper pair creation and annihilation operators do not obey Bose-Einstein commutation relations.

However, the Cooper pair can still qualitatively thought of as a pseudo-boson that undergoes pseud0-BEC, and this picture is indeed  very useful. It enabled the prediction of pseud0-BEC in neutron stars, liquid 3-helium and ultra-cold fermionic gases — predictions which now have firm experimental backing.

An interesting note is that one can study this BCS-to-BEC crossover in ultracold Fermi gases and go from the overlapping to non-overlapping limit by tuning the interaction between atoms and I’ll try to write a post about this in the near future.

So while BCS theory has many attributes that make it important, to my mind, the most profound thing is that it presents a mechanism by which weakly interacting fermionic pairs can condense into a pseudo-BEC. This is not at all obvious, but indeed what happens in nature.

Update: In light of the description above, it seems surprising that the temperature at which Cooper pairs form is the same temperature at which they seem to condense into a pseudo-BEC. Why this is the case is not obvious and I think is an open question, especially with regards to the cuprates and in particular the pseudogap.

## 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.