Plutonium: a case study in why CM physics is rich

At the heart of condensed matter physics are two key concepts: the emergence of rich phenomena (including spontaneously occurring order - structural, magnetic, or otherwise) in the many-particle limit; and the critical role played by quantum mechanics in describing the many-body states of the system. I've tried to explain this before to lay persons by pointing out that while complicated electronic structure techniques can do an adequate job of describing the electronic and vibrational properties of a single water molecule at zero temperature, we still have a difficult time predicting really emergent properties, such as phase diagram of liquid, solid, and vapor water, or the viscosity or surface tension of liquid water.

Plutonium is an even more striking example, given that we cannot even understand its properties from first principle when we only have a single type of atom to worry about. The thermodynamic phase diagram of plutonium is very complicated, with seven different crystal structures known, depending on temperature and pressure. Moreover, as a resident of the actinide row of the periodic table, Pu has unpaired 5f electrons, though it is not magnetically ordered. At the same time, Pu is very heavy, with 94 total electrons, so that relativistic spin-orbit effects can't be neglected in trying to understand its structure. The most sophisticated electronic structure techniques out there can't handle this combination of circumstances. It's rather humbling that more than 70 years after its discovery/synthesis, we still can't understand this material, despite the many thousands of person-hours spent on it via various nations' nuclear weapons programs.

Einstein, thermodynamics, and elegance

Recently, in the course of other writing I've been doing, I again came to the topic of what are called Einstein A and B coefficients, and it struck me again that this has to be one of the most elegant, clever physics arguments ever made.  It's also conceptually simple enough that I think it can be explained to nonexperts, so I'm going to give it a shot.

Ninety-four years ago, one of the most shocking ideas in physics was the concept of the spontaneous, apparently random, breakdown of an atomic system.  Radioactive decay is one example, but even light emission from an atom in an excited state will serve.  Take ten hydrogen atoms, all in their first electronically excited state (electron kicked up into a 2p orbital from the 1s orbital).  These will decay back into the 1s ground state (spitting out a photon) at some average rate, but each one will decay independently of the others, and most likely at a different moment in time.  To people brought up in the Newtonian clockwork universe, this was shocking.  How could truly identical atoms have individually differing emission times?  Where does the randomness come from, and can we ever hope to calculate the rate of spontaneous emission?

Around this time (1917), Einstein made a typically brilliant argument:  While we do not yet know [in 1917] how to calculate the rate at which the atoms transition from the ground state "a" to the excited state "b" when we shine light on them (the absorption rate), we can reason that the rate of atoms going from a to b should be proportional to the number of atoms in the ground state (N_a) and the amount of energy density in the light available at the right frequency (u(f)).  That is, the rate of transitions "up" = B_ab N_a u(f), where B is some number that can at least be measured in experiments.  [It turns out that people figured out how to calculate B using perturbation theory in quantum mechanics about ten years later.].  Einstein also figured that there should be an inverse process (stimulated emission), that causes transitions downward from b to a, with a rate = B_ba N_b u(f).  However, there is also the spontaneous emission rate = A_baN_b, where he introduced the A coefficient.

Here is the brilliance.  Einstein considered the case of thermal equilibrium between atoms and radiation in some cavity.  In steady state, the rate of transitions from a to b must equal the rate of transitions from b to a - in steady state, no atoms are piling up in the ground or excited states.  Moreover, from thermodynamics, in thermal equilibrium, the ratio of N_b to N_a should just be a Boltzmann factor, exp(-E_ab/k_BT), where E_ab is the energy difference between the two states, k_B is Boltzmann's constant, and T is the temperature.  From this, Einstein shows that the two Bs were equal, was able to solve for the unknown A in terms of B (which can be measured and nowdays calculated), and to show that the energy density of the radiation (u(f,T)) is Planck's blackbody formula.

My feeble writing here doesn't do this justice.  The point is, from basic thermodynamic reasoning, Einstein made it possible to derive an expression for the spontaneous emission rate of atoms, many years in advance of the theory (quantum electrodynamics) that allows one to calculate it directly.  This is what people mean by the elegance of physics - in a few pages, from proper reasoning on fundamental grounds, Einstein was able to deduce relationships that had to exist between different physical parameters; and these parameters could be measured and tested experimentally.  For more on this, here is a page at MIT that links to a great Physics Today article about the topic, and an English translation of Einstein's 1917 paper.  

Slackers, coasters, and sherpas, oh my.

This is mostly for my American readers - be forewarned.

I wrote last year about a plan put forward by Rick O'Donnell, a controversial "consultant" hired by the state of Texas (hint: Gov. Rick Perry, apparent 2012 presidential hopeful, wanted this guy.) to study the way public universities work in Texas. Specifically, O'Donnell came from a think tank that had very firm predetermined concept about higher education: Faculty are overpaid slackers that are ripping off students, and research is not of value in the educational environment. O'Donnell has written a report (pdf) about this topic, and he's shocked, shocked to find that he was absolutely right. By his metrics of number of students taught and research dollars brought in, he grouped faculty at UT and Texas A&M into "Dodgers, Coasters, Sherpas, Pioneers, and Stars". Pioneers are the people who bring in big grants and buy out of teaching. Stars are the people who bring in grants and teach large lecture classes. Sherpas are mostly instructors (he doesn't seem to differentiate between instructors and faculty) who lecture to large classes but don't bring in grants. Dodgers teach small classes and don't bring in grant money. Coasters teach small classes and bring in some grant money.

This is the exact incarnation of what I warned about in comments on my old post. This analysis basically declares that all social science and humanities faculty that teach upper division classes are worthless leeches (small classes, no grants) sponging off the university. People in the sciences and engineering who teach upper level classes aren't any better, unless they're bringing in multiple large research grants. Oh, and apparently the only metric for research and scholarship is money.

Nice. Perry, by the way, also appointed Barbara Cargill to run the state board of education. She's a biologist who wants evolution's perceived weaknesses to be emphasized in public schools, and she also was upset because the school board only has "six true conservative Christians" as members. I guess Jews, Muslims, Buddhists, Hindus, and atheists need not apply.  Update:  It looks like Texas has dodged creationism for another couple of years.  Whew.

What is so hard about understanding high temperature superconductivity?

As ZZ has pointed out, Nature is running a feature article on the history of high temperature superconductivity over the last 25 years. I remember blogging about this topic five years ago when Nature Physics ran an excellent special issue on the subject. At the time, I wrote a brief summary of the field, and I've touched on this topic a few times in the intervening years. Over that time, it's pretty clear that the most important event was the discovery of the iron-based high temperature superconductors. It showed that there are additional whole families of high temperature superconducting materials that are not all copper oxides.

Now is a reasonable time to ask again, what is so hard about this problem? Why don't we have a general theory of high temperature superconductivity?  Here are my opinions, and I'd be happy for more from the readers.

• First, be patient.  Low-T superconductivity was discovered in 1911, and we didn't have a decent theory until 1957.  By that metric, we shouldn't start getting annoyed until 2032.  I'm not just being flippant here.  The high-Tc materials are generally complicated (with a few exceptions) structurally, with large unit cells, and lots of disorder associated with chemical doping.  This is very different than the situation in, e.g., lead or niobium.
• Electron-electron interactions seem to be very important in describing the normal state of these materials.  In the low-Tc superconductors, we really can get very far understanding the normal starting point.  Aluminum is a classic metal, and you can do a pretty good job getting quantitative accuracy on its properties from the theory side even in single-particle, non-interacting treatments (basic band theory).  In contrast, the high-Tc material normal states are tricky.  Heck, the copper oxide parent compound is a Mott insulator - a system that single-particle band structure tells you should be a metal, but is in fact insulating because of the electron-electron repulsion!  
• Spin seems to be important, too.   In the low-Tc systems, spin is unimportant in the normal state, and the electrons pair up so that each electron is paired with one of opposite spin, so that the net spin of the pair is zero, but that's about it.  In high-Tc systems, on the other hand, very often the normal state involves magnetic order of some sort, and spin-spin interactions may well be important.
• Sample quality has been a persistent challenge (particularly in the early days).
• The analytical techniques that exist tend to be indirect or invasive, at least compared to the desired thought experiments.  This is a persistent challenge in condensed matter physics.  You can't just go and yank on a particular electron to see what else moves, in an effort to unravel the "glue" that holds pairs together (though the photoemission community might disagree).  While the order parameter (describing the superconducting state) may vary microscopically in magnitude, sign, and phase, you can't just order up a gadget to measure, e.g., phase as a function of position within a sample.  Instead, experimentalists are forced to be more baroque and more clever.
• Computational methods are good, but not that good.  Exact solutions of systems of large numbers of interacting electrons remain elusive and computationally extremely expensive.  Properly dealing with strong electronic correlations, finite temperature, etc. are all challenges.

Still, it's a beguiling problem, and now is an exciting time - because of the iron compounds, there are probably more people working on novel superconductors than at any time since the heady days of the late '80s, and they're working with the benefit of all that experience and hindsight.  Maybe I won't have to write something like this for the 30th high-Tc anniversary in 2016....

Updated look.

I finally bit the bullet and updated the look of the blog.  I'm still keeping it ad-free, though.

google+

I have a nagging feeling that google+ could somehow be used to significantly increase readership of my blog, if only I was appropriately savvy.  Anyone have any suggestions or thoughts on this?  I don't crave the attention per se, but I'd be fibbing if I said I wasn't jealous of the readership numbers of the folks that blog at, e.g., scienceblogs, discovermagazine.com, or scientificamerican.com.  Larger readership would undoubtedly motivate more writing, too, though that's not necessarily great for my time management....

It's all at the interface. Again.

Over the last decade, there has been a great deal of exciting work in making electronically interesting systems at atomically sharp interfaces between different oxide materials (oxide heterostructures). Analogous efforts at semiconductor-dielectric interfaces have given us the conventional field-effect transistor, something like 10⁹ of which are being used to render this page for you. Likewise, heterointerfaces in compound semiconductor systems (especially the technologically relevant III-V materials like GaAs) have given us two Nobel Prizes and a great deal of quantum electronic fun. Oxides are much trickier beasts from the materials science side, making growth and interfacial control a major challenge. Moreover, with respect to basic science, transition metal oxides can be incredibly rich systems, because in many of them electron-electron interactions lead to competing electronic and magnetic phases, with consequences like the emergence of high temperature superconductivity.

A few years ago, this paper demonstrated that it was possible to get superconductivity at the interface between SrTiO₃ and LaAlO₃, two oxides that are both insulating if perfectly stoichiometric. Still, SrTiO₃ is known to superconduct if highly doped, and therefore this observation, while a great experiment, wasn't hugely shocking, given the existence of a high density electron gas at the STO/LAO interface. More recently, this paper showed that high temperature superconductivity could happen at the interface between a nominally insulating oxide and a metallic (but not superconducting) cuprate related to the high-Tc materials. This past week on the arxiv, a logical successor to these works appeared here. The authors use two nominally insulating oxides (STO again, and CaCuO₂. Because of imperfect stoichiometry at the interface (excess oxygen, apparently), there is a conducting layer at the interface, with a superconducting transition around 50 K (in one sample, though others all show transitions exceeding 25 K). Bearing in mind that this is a preprint (and therefore has not been refereed), it is still very exciting. We are finally approaching the ability to engineer complex materials (not just semiconductors) on the atomic layer level, and this should be an incredible playground for basic science and materials engineering. It'd be great to get plugged into a collaboration working in this area.

Science and the public

I couldn't help but notice that one of my favorite producers of animated films, Aardman Animation, is coming out with a new movie (trailer here). I find it very interesting that the UK version of the movie is "The Pirates! In an Adventure with Scientists!", while the US version is "The Pirates! Band of Misfits!". The film is based on a book with the former title, by the way. I don't want to overanalyze this, but it's hard to escape the conclusion that some marketing drone decided, "scientist" is box-office poison, and that "misfit" was an acceptable and more marketable substitute in the US. Great. Wonderful. In case you're wondering, Charles Darwin shows up as a character in the book/movie. I imagine that the US ads won't be playing that up very much, or there will be protests. Sigh.

(I do have a science post I'll make shortly. I just couldn't let this pass w/o comment. And it's taking enormous self-restraint not to launch into extended political invective about the US, but there are many places where people can read that if they want to.)

Follow-up, and blogger drop-off

Regarding the story mentioned here, Nature has published both a provocative and interesting article by Eugenie Reich about the larger issues raised, and an editorial. Sorry that these are behind a pay-wall. To summarize in a few sentences: Eugenie Reich points out that the misconduct investigation relevant to this discussion highlights important problems with the US Department of Energy's handling of such cases. To wit: There are issues of independence and chain of authority of the investigators, and lack of proper record keeping, documentation, etc. of investigation reports. The conclusion is that this is a powerful argument for the DOE to establish an Office of Research Integrity, like those in some other agencies. The editorial from Nature chastises the DOE along these lines. Interesting that the Nature editorial makes no mention at all of their own role in not publishing technical comments relevant to this particular matter.

In blogging news, there has been a drop-off in the number of active physical science bloggers. David Bacon's Quantum Pontiff has decohered. The Incoherent Ponderer has gone so far as to apparently delete his entire blog and blogger profile. Other blogs have not been updated in many months. It's likely that this is all part of a natural stabilization of blogging - people run out of things to say, and the novelty of blogging has trailed off. It will be interesting to see where this trend resolves. It'll be a shame to have fewer interesting voices to follow, though. (Clearly we should all switch to Twitter, since 140 characters should be more than sufficient to carry out detailed science discussions or popularizations for the lay audience. Ahem.)

Crowd-sourcing, video games, and the world's problems

This past weekend, I caught a snippet of a rebroadcast of this NPR story about Jane McGonigal and the thesis of her recent book. In short, she points out that as a species we have spent literally millions of person-years playing World of Warcraft, an online game that involves teamwork and puzzle-solving (as well as all the usual fun silliness of videogames). Her point is that in the game environment, people have demonstrated great creativity as well as a willingness to keep coming back, over and over, to tackle challenging problems (in part because there is recognition by the players that problems are pitched at a level that is tricky but not insurmountable). She wants to harness this kind of intellectual output for good, rather than just have it as a social (or antisocial) outlet. She's not the first person to have this sort of idea, of course (see, e.g., Ender's Game, or the Timothy Zahn short story "The Challenge"), but the WoW numbers are truly eye-popping.

It would be great if there were certain scientific problems to which this could be applied. The overall concept seems easiest to adapt to logistics (e.g., coming up with clever ways of routing shipping containers or disaster relief supplies), since that's a puzzle-solving subdiscipline where the basic problems are at least accessible to lay-people. Trying this with meaty scientific challenges would be much more difficult, unless those challenges could be translated effectively into problems that don't require years and years of foreknowledge. Hmm. Still very thought-provoking.

The tyranny of the buried interface

Time and again, a major impediment to research progress in condensed matter physics, electrical engineering, materials science, and physical chemistry is the need to understand what is happening in some system at a buried interface. For example, in organic photovoltaic devices, it is of great importance to learn more about what is happening at metal/organic semiconductor interfaces (charge transfer, interfacial dipole formation, Fermi level pinning) and organic/organic interfaces (exciton splitting at the interface between electron- and hole-transporting materials). Another example: in lithium ion batteries, at the interface between either the cathode or the anode and the electrolyte, after the first couple of charge and discharge cycles, there forms the "solid electrolyte interface" (SEI) layer. The SEI is nanoscale in thickness, stabilizes the electrode surface, establishes the energetic lineup between the electrolyte redox chemistry and the actual electrode surface, strongly affects the kinetics of the lithium ion transport, etc.

Unfortunately, probing buried interfaces in situ in functioning systems is extremely hard. There generally is no Star Trek scanner device that can nondestructively reveal atomic-scale details of buried 3d structures. Many of our best characterization approaches are surface-based, or require thinned down samples, and there are always difficult questions about how information gained in such investigations translates to the real situation of interest. This is not a new problem. From the early days of surface science and before, people have been worrying about, e.g., how to connect studies performed in UHV on single crystal surfaces with "real world" situations on polycrystalline surfaces with ambient contaminants. There are some macro-scale interface sensitive approaches (exploiting x-ray standing waves, or interfacial optical effects). Still, the more people working on developing better characterization tools toward this end, the better, even if it doesn't sound terribly exciting to the masses.