Monthly Archives: May 2015

Beckett and Science

Samuel Beckett. A question that always arose for me when reading Beckett’s works, especially Endgame, was: does technology make people happier? In Endgame, the setting is a bunker after some sort of nuclear holocaust and the protagonist looks outside to see “only grey”.

In the aftermath of the World War II, when this play was written, there seemed to be a deep skepticism among literary and artistic circles of the benefit of technology in society. Having witnessed the massive scale of casualties, it is easy to see why Beckett may have thought this way as well (though he was a recluse and rarely gave interviews, so it is hard to know for sure).

The advantages of technology are obvious — enabling humans to live for longer, fighting disease, spurring economic progress, etc. However, I don’t believe that these benefits address the question as to whether people are happier because of it.

I realize that this is seemingly hypocritical coming from an experimental physicist whose life depends partly on driving technological progress, but I cannot help but face Beckett’s question with uncertainty.

What THE WIRE Taught Me About Science

The famous HBO series, The Wire, which many have called the greatest television show of all time (e.g. here and here), has a lot to say about urban decay, race relations, and the structure of power and organizations . There is one theme that is particularly relevant to us in the sciences that The Wire profoundly addresses: the competition between careerism and good work.

In the series, many that get promoted in the hierarchical structure of the police department are not the best policemen, but the ones that are the most career-oriented. In one of the more memorable quotes on the show (even though there are so many!), Lt. Daniels says to Detective Carver, who is about to be promoted:

Couple weeks from now, you’re gonna be in some district somewhere with 11 or 12 uniforms looking to you for everything. And some of them are gonna be good police. Some of them are gonna be young and stupid. A few are gonna be pieces of shit. But all of them will take their cue from you. You show loyalty, they learn loyalty. You show them it’s about the work, it’ll be about the work. You show them some other kinda game, then that’s the game they’ll play. I came on in the Eastern, and there was a piece-of-shit lieutenant hoping to be a captain, piece-of-shit sergeants hoping to be lieutenants. Pretty soon we had piece-of-shit patrolmen trying to figure the job for themselves. And some of what happens then is hard as hell to live down. Comes a day you’re gonna have to decide whether it’s about you or about the work.

There is advice there for both advisers and students alike.

Advisers: (1) Pick students whose motivations lie in doing good work. (2) Show your students that what you do is about the work, about producing good science and not about publishing x hurried papers. (3) Help your students careers (honestly and without too much hype) when they aren’t looking (e.g. nominate them for awards, talk them up when you get the chance, etc.).

Students: (1) The adviser you pick will ultimately have a strong influence on where you end up and how you think about science in general; choose wisely. (2) Ask older graduate students, postdocs and professors questions; a large part of scientific development is figuring how/where to find interesting problems. (3) Do good work: Do not cut corners, do not hurriedly publish, be thorough and do not be dishonest.

In The Wire, there is a constant battle between the higher-ranked officials in the police department (who want to bring in low-level drug dealers under pressure from even higher-ranked officials and politicians), and the lower-ranked officials (who want to work a case until the entire case is solved so that they can bring in the drug kingpin and not just low-level middlemen). Fight the pressure to publish (to the best of your ability), and publish well when you do (sorry if you can’t see the analogy here!)

Alright, I’ll get off the soapbox now and just make one last comment: I have tried my best to follow these principles in graduate school (and have not always succeeded), but I do still think The Wire outlines a simple code to follow.

In the end, even in a show as pessimistic as The Wire, often good police got promoted and did their jobs better than the career-oriented ones. It is possible to do good work and survive even in this academic climate.

Also, if you’re a fan of The Wire, I recommend reading this: http://aaronhuertas.com/2011/11/what-i-learned-from-watching-the-wire-three-times/

Floquet States on Topological Insulator Surfaces

In a very beautiful 2013 paper by the Gedik group (click here for arXiv link) at MIT, they observed Floquet states on the surface of topological insulator Bi_2Se_3 using angle-resolved photoemission.

In the experiment, they applied a potential by applying an intense laser pulse (what is more time-periodic than light?!). As solid state physicists we are familiar with what happens when one applies a periodic potential in space, and the mathematical structure here is identical. The analogy is made concrete below:

Periodicity in space: \textbf{k} = \textbf{k}+\textbf{G}

Periodicity in time: E(\textbf{k}) = E(\textbf{k}) + \hbar\omega

There is a beautiful visualization of this periodicity in the paper as seen below (click to enlarge):

GedikFloquet

One can see the repetition in \hbar\omega (in A and B in the figure) as determined by the frequency of the incoming laser pulse. Furthermore, one can see the bands interacting with each other and causing gaps to open up as pictured in the schematic on the right and in the data in C and D in the figure.

A very simple idea, a very elegant experiment.

Was the Higgs Boson Discovered in 1980?

In a tour-de-force experiment in 1980, Klein and Sooryakumar discovered a collective mode in the superconducting phase of NbSe_2 in a Raman experiment. This mode interacts with the collective mode of the charge density wave and was interpreted a few year later by Littlewood and Varma to be a Higgs amplitude mode of the superconducting state.

Could it really be said that the Higgs mode was discovered in Urbana in 1980?

Of course, I am being facetious, but it is a rather cute historical curiosity. That being said, I have to also admit that I am not 100% convinced that this interpretation is correct, though it does carry some weight.

This classic experiment has also been driving experiments recently towards observing the Higgs mode in other superconducting systems as well. For example, click here and here.

The other part of this experiment that makes it particularly relevant to current studies is the observation of an interaction between superconductivity and charge density waves as was mentioned in a previous post. With the application of a magnetic field, they were able to suppress the superconductivity and enhance the charge density wave collective excitation as pictured below.

SooryakumarAndKlein

How do we define states of matter?

Historically, many people seemed to lean towards defining a phase of matter by its (broken) symmetries. For instance, a ferromagnet has broken rotational symmetry and time-reversal symmetry, a solid has broken translational and rotational symmetry, etc. In light of the discoveries of the Quantum Hall Effect and topological insulators, it seems like this symmetry classification does not encompass all states of matter.

The symmetry classification is largely a theoretical construct, however. I would think that one defines a state of matter by particular experimental properties that it exhibits. For example, one could define a superconductor by requiring it to exhibit the following:

  1. Zero Resistivity
  2. Meissner Effect
  3. Zero Peltier Coefficient

Put another way, to verify that one has discovered a superconductor, these three criteria must be satisfied.

Let us take another example: a simple metal. The criterion that must be satisfied for this case is the existence of a Fermi surface. This can be measured by quantum oscillation measurements, angle-resolved photoemission, or a few other probes.

Yet another example: a 2D topological insulator. What one must observe is:

  1. The Fermi energy intersects an odd number of topologically protected edge states in half the edge Brillouin zone (which was shown by transport in this classic paper)
  2. The existence of a spin-polarization associated with the edge states

While these three examples were chosen because they were simple, I have remaining doubts. Are these observations necessary and sufficient to define these states of matter? Are there cases where one can better define a state of matter theoretically?

For instance, a theorist may define a 2D topological insulator by the existence of a non-trivial topological number, which seems like a perfectly valid criterion to me. This topological number cannot be experimentally observed in a very direct way (to my knowledge) and has to be inferred from the edge states, band structure, etc.

The reason I started thinking about this is because I did not find the definition of a charge density wave in this widely-cited paper by Johannes and Mazin appropriate. It states:

[A charge density wave is a] Peierls-like instabilit[y] that occur[s] due to a divergency in the real part of the electronic susceptibility, so that the electronic subsystem would be unstable per se, even if the ions were clamped at their high symmetry positions.

This definition bothers me in particular because it defines a charge density wave by its cause (i.e. Peierls-like instability due to a divergence in the real part of the electronic susceptibility).  The main qualm I have is that one should not define a state of matter by its origin or cause. This is like trying define a superconductor by the mechanism that causes its existence (i.e. phonon-mediated electron-electron interaction for superconductors, which would exclude unconventional superconductors from its definition). This is obviously problematic. Therefore, shouldn’t one define a charge density wave by its experimentally measured properties?

So I come back to the original question: how does one define a state of matter?

Comments welcome…