good grief.

I don't know what's more mortifying: this story, or the possibility that the Senate will strip NSF funding out of the stimulus bill because of the actions of a small number of idiots.

Colbert on science policy

This was very funny. For those not in the US, my apologies that the video doesn't work. It's Stephen Colbert talking about science policy under the Bush administration and then interviewing Chris Mooney.

This article in the NY Times was also very good.

What is a polaron?

This is another attempt to explain a condensed matter physics concept in comparatively nontechnical language. Comments are, as always, appreciated.

One common example of a quasiparticle is the polaron. When a charge carrier (an electron or hole) is placed into a solid, the surrounding ions can interact with it (e.g., positive ions will be slightly attracted to a negatively charged carrier). The ions can adjust their positions slightly, balancing their interactions with the charge carrier and the forces that hold the ions in their regular places. This adjustment of positions leads to a polarization locally centered on the charge carrier. The combo of the carrier + the surrounding polarization is a polaron. There are "large" and "small" polarons, defined by whether or not the polarization cloud is much larger than the atomic spacing in the material. Polarons are a useful way of thinking about carriers in ionic crystals, materials with "soft" vibrational modes (such as the manganites), and organic semiconductors (very squishy, deformable systems held together by van der Waals rather than covalent bonding).

Not content to let the general relativity fans have all the fun, I can describe this with a ball-rolling-on-a-rubber-sheet analogy. The ball is the charge carrier; the deformation of the rubber sheet is the polarization "cloud". Consider tilting the rubber sheet - this is analogous to applying an electric field to the material. The ball will roll in response to the tilt, but it will be slowed down compared to how it would roll on a hard tilted surface, since it has to put energy into deforming the sheet. In real materials, this shows up as a correction to the effective mass of the charge carrier. All other things being equal, polarons are heavy compared to bare quasiparticles.

We can carry this analogy further. Suppose we have two balls on the rubber sheet. In this classical picture, if the balls are so close together that their sheet deformations touch, the balls will be attracted together and end up in one deformation, held apart by their mutual hard-core repulsion. This is a crude analogy for bipolaron formation, which does happen in real materials. (Though, in real bipolarons the (purely quantum mechanical) spins of the individual polarons are important to stabilizing the bipolaron. The spins form a singlet....) Furthermore, suppose the rubber sheet takes some time to respond to the balls, and takes some time to restore itself to its undeformed state once a ball passes by. You can picture a ball rolling in some direction, leaving behind itself a little groove in the sheet that "fills in" at some rate. This would lower the energy of some other ball if that other ball were traveling in, say, the exact opposite direction of the first ball. This is a very crude way of thinking about the attractive pairing interaction between electrons in low temperature superconductors.

Finally, suppose the rubber sheet is really stretchy. A ball dropped on the sheet will pull the sheet down so far that it'll look like a little punching bag. Now if you try to tilt the sheet, the sheet will have stretched so tightly that the ball won't want to roll at all. Instead, the little punching bag will hang there at an angle relative to the sheet. Something analogous to this can happen in real materials, too - polarons can self-trap. That is, the charge carrier deforms the local environment so much that it basically digs itself such a deep potential well that it can't move anymore. Chemists have their own name for this, by the way. A molecule that deforms to self-trap an extra electron is a radical anion, and a molecule that deforms to self-trap a hole is a radical cation.

"Science" and inaugural addresses

Yesterday, as a bunch of us gathered in an office to watch the Inauguration, after President Obama's line about science ("We will restore science to its rightful place...."), I said that I'd bet that was the only time science had been mentioned in an inaugural address. Well, thanks to this impressive website, I now know that I was quite wrong. The word "science" has appeared 22 times in 15 different inaugural addresses. These uses include John Adams back in 1797 (in one of the biggest run-on sentences I've seen since the last time I read a Virginia Woolf novel) encouraging the founding of universities, FDR worrying about science run amok ("For, without [government aid], we had been unable to create those moral controls over the services of science which are necessary to make science a useful servant instead of a ruthless master of mankind."), and Kennedy wanting to use science to thaw US-Soviet relations ("Let both sides seek to invoke the wonders of science instead of its terrors") and forestall nuclear war ("the dark powers of destruction unleashed by science"). Interesting stuff. By the way, I'll save you the trouble of looking. No president has ever said "physics" in an inaugural address.

Science in the stimulus.

For those interested, here is a link to the executive summary of the (Democratic draft of the House version) of the forthcoming economic stimulus bill. The science portions are easy to find in there, and I like what I see.

Update. The science policy bloggers for Science have an article that basically points to this analysis of the proposed stimulus by the AAAS. The two big questions that come to mind are, (1) will there be sustained support for science to follow up on this investment of resources?; and (2) how will the details work regarding the requirements that the funds be allocated quickly?

What are quasiparticles?

The word quasiparticle is a term of art that condensed matter physics types throw around quite a bit. What does is it really mean? I'll describe one analogy that may be useful, and then give a more rigorous definition. Suppose you had a bin filled up to some height with rubber balls of uniform size. The lowest energy ("ground") state of this would be the one with the balls pretty much forming a close-packed structure, all stacked up. If you took one ball from somewhere and set it on top of the others, that would cost a little bit of energy, because the ball has some mass acted on by gravity and it takes work to lift it up. This one ball popped up above the rest is not exactly a quasiparticle. Notice that it's not really the same as an isolated ball. It's a bit deformed from interactions with the balls underneath it, since it has weight and the balls are all a little squishy. Similarly, if you took a step back and looked really carefully, you'd see that the balls right under that one have all had to rearrange themselves a little. The whole package (popped-up ball + deformations + rearrangement of the positions of the neighboring balls) is analogous to a quasiparticle, since you can't really have some parts without the others. In condensed matter physics, a fancier scientific definition would be: "a low energy excitation of a system, possessing a set of quantum numbers and/or well-defined expectation values of certain operators (position, charge, momentum, angular momentum, energy) often associated with isolated particles."

More postings soon, but looming deadlines may mean a slow-down.

What does it mean for a material to be a "metal"?

Continuing on from my earlier posts about insulators, it's worth thinking about what we mean by a "metallic" state. Colloquially, people have an image of what they think is a metal: a material that is shiny, electrically conducting, and probably relatively ductile and malleable. Let's not discuss the elastic properties at the moment, since their origin is rather subtle. The electrical conduction is what really stands in contrast to insulators, and the shiny surface is a consequence of the electrical conduction at high frequencies (optical, ~ 10¹⁵ Hz). (By the way, for those interested in why some metals have color to them, this site has a pretty nice explanation. The short answer: interband transitions alter the absorption at short wavelengths.)

It's important to understand that, from the condensed matter physicist's perspective, there's a big difference between a substance that is merely electrically conductive and one that is a "real" metal. In a real metal, the electrical resistivity decreases as temperature is decreased. There are conduction mechanisms (e.g., ionic conduction in glasses; hopping conduction in doped organic semiconductors) that become much less effective at lower temperatures - those systems are not metals, just moderately conducting at room temperature. Similarly, lightly doped semiconductors aren't metals either; as T approaches 0 they have no mobile charge carriers. It would be nice to be able to find a ground state property that lets us decide whether something is a metal or an insulator rather than worrying about temperature dependences. Fortunately, there is. As discussed here (a nice pdf that I found while learning more about what Peter had written in the comments to the previous post), when placed between capacitor plates at T = 0, a metal develops only a surface charge, while an insulator develops a bulk dielectric polarization (dipole moment per unit volume) throughout itself.

There are different types of metals. Conventional metals are Landau Fermi liquids. The low energy electronic excitations of Fermi liquids are "quasiparticles" that act very much like non-interacting electrons - they have spin-1/2, charge -e, and have a lifetime much longer than h/k_BT. In bulk Fermi liquids, electronic excitations can have arbitrarily low energies. The spectrum of these excitations is said to be gapless. The hallmark of Fermi liquids is that they have properties that look much like those we find in undergrad statistical mechanics treatments of noninteracting Fermi gases. For example, their heat capacities vary at low temperatures as T, and their resistivities vary at low temperatures as T².

There are other metallic states known variously as bad metals or strange metals. The classic example of a bad metal is the normal state of optimally doped high temperature superconductors. These systems have a metallic ground state, but near T = 0, their resistivities vary linearly in T rather than quadratically. This may not seem like a big deal, but it has major implications. It implies that the low energy electronic excitations of these materials are not well described as quasiparticles; they must somehow involve collective excitations of many correlated electrons, and may not have easily intuitive quantum numbers. That is, they're non-Fermi liquids. Trying to understand these systems and their excitations is a major outstanding challenge in condensed matter physics today. It's hard because it involves understanding excitations of a system of many strongly interacting quantum particles, and also because our intuition has been shaped by our classical ideas about simple quasiparticles. By the way, this idea of excitations that are complicated and lack particle-like quantum numbers has come into vogue in high energy physics in the form of "unparticles".

More about insulators

I've been thinking more about explaining what we mean by "insulators", in light of some of the insightful comments. As I'd said, we can think about three major classes of insulators: band insulators (a large gap due to single-particle effects (more below) exists in the ladder of electronic states above the highest occupied state); Anderson insulators (the highest occupied electronic states are localized in space, rather than extending over large distances; localization happens because of disorder and quantum interference); and Mott insulators (hitherto neglected electron-electron interactions make the energetic cost of moving electrons prohibitively high).

The idea of an energy gap (a big interval in the ladder of states, with the states below the gap filled and the states above the gap empty) turns out to be a unifying concept that can tie all three of these categories together. In the band insulator case, the states are pretty much single-particle states (that is, the energy of each state is dominated by the kinetic energies of single electrons and their interactions with the ions that supply the electrons). In the Anderson insulator case, the gap is really the difference in energy between the highest occupied state and the nearest extended state (called the mobility edge). In the Mott case, the states in question are many-body states that have a major contribution due to electron-electron interactions. The electron-electron interaction cost associated with moving electrons around is again an energy gap (a Mott gap), in the ladder of many-body (rather than single-particle) states.

I could also turn this around and talk in terms of the local vs. extended character of the highest occupied states (as Peter points out). In the ideal (infinite periodic solid) band insulator case, all (single-particle) electronic states are extended, and it's the particular lattice arrangement and electronic population that determines whether the highest occupied state is far from the nearest unoccupied state. In the Anderson case, quantum interference + disorder leads to the highest occupied states looking like standing waves - localized in space. In the Mott case, it's tricky to try to think about many-body states in terms of projections onto single-particle states, but you can do so, and you again find that the highest relevant states are localized (due, it turns out, to interactions). Like Peter, I also have been meaning to spend more time thinking hard about insulators.

Coming soon: a discussion of "metals".

Faraday

It's a small world. Just last week I finished reading this book, a very nice biography of Michael Faraday, possibly the greatest experimental physicist ever. Lo and behold, this week there are two long blog postings (here and here) also talking about Faraday. What an impressive scientist. Now I need to find a good bio of Maxwell....

What does it mean for a material to be an "insulator"?

I've been thinking for a while about trying to explain some physics concepts on, well, a slightly more popular level. This is a first pass at this, focusing on electrical insulators. Feedback is invited. I know that this won't be perfect for nonscientists at a first cut.

Very often we care about the electrical properties of materials. Conceptually, we imagine hooking the positive terminal of a battery up to one end of a material, hooking the negative terminal up to the other end, and checking to see if any current is flowing. We broadly lump solids into two groups, those that conduct electricity and those that don't. Materials in the latter category are known as insulators, and it turns out that there are at least three different kinds.

• Band insulators. One useful way of thinking about electrons in solids is to think about the electrons as filling up single-particle states (typically with two electrons per state). This is like what you learn in high school chemistry, where you're taught that there are certain orbitals within atoms that get filled up, two electrons per orbital. Helium has two electrons in the 1s orbital, for example. In solids, there are many, many states, each one with an associated energy cost for being occupied by an electron, and the states are grouped into bands separated by intervals of energy (band gaps) with no states. (Picture a ladder with groups of closely spaced rungs, and each rung has two little divots where marbles (the electrons) can sit.) Now, in clean materials, you can think of some states as corresponding to electrons moving to the left. Some states correspond to electrons moving to the right. In order to get a net flow of electrons when a battery is used to apply a voltage difference across a slab of material, there have to be transitions that, for example, take electrons out of left-moving states and put them into right-moving states, so that more electrons are going one way than the other. For this to happen, there have to be empty states available for the electrons to occupy, and the net energy cost of shifting the electrons around has to be low enough that it's supplied by the battery or by thermal energy. In a band insulator, all of the states in a particular band (usually called the valence band) are filled, and the energetically closest empty states are too far away energetically to be reached. (In the ladder analogy, the next empty rung is waaay far up the ladder.) This is the situation in materials like diamond, quartz, and sapphire.
  
• Anderson insulators. These are materials where disorder is responsible for insulating behavior. In the ladder analogy above, each rung of the ladder corresponded to what we would call an "extended" state. To get a picture of what this means, consider looking at a smooth, grooved surface, like a freshly plowed field, and filling it partially with water. Each furrow would be an extended state, since on a level field water would extend along the furrow from one end of the field to the other. Now, a disordered system in this analogy would look more like a field pockmarked with hills and holes. Water (representing the electrons) would pool in the low spots rather than forming a continuous line from one end of the field to the other. These local low spots are defects, and the puddles of water correspond to localized states. In the real quantum situation things are a bit more complicated. Because of the wavelike nature of electrons, even weak disorder (shallow dips rather than deep holes in the field) can lead to reflections and interference effects that can cause states to be localized on a big enough "field". Systems like this are insulating (at least at low temperatures) because it takes energy to hop electrons from one puddle to another puddle. For small applied voltages, nothing happens (though clearly if one imagines tilting the whole field enough, all the water will run down hill - this would correspond to applying a large electric field.). Examples of this kind of insulating behavior include doped polymer semiconductors.
  
• Mott insulators. Notice that nowhere in the discussion of band or Anderson insulators did I say anything at all about the fact that electrons repel each other. Electron-electron interactions were essentially irrelevant to those two ways of having an insulator. To understand Mott insulators, think about trying to pack ping-pong balls closely in a 2d array. The balls form a triangular lattice. Now the repulsion of the electrons is represented by the fact that you can't force two ping-pong balls to occupy the same site in the 2d lattice. Even though you "should" be able to put two balls (electrons) per site, the repulsion of the electrons prevents you from doing so without comparatively great energetic cost (associated with smashing a ping-pong ball). The result is, for exactly 1 ball (electron) per site ("half-filled band") in this situation dominated by ball-ball interactions ("on-site repulsion"), no balls are able to move in response to an applied push (electric field). To get motion (conduction) in this case, one approach is to remove some of the balls (electrons) to create vacancies in the lattice. This can be done via chemical doping. Examples of Mott insulators are some transition metal oxides like V₂O₃ and the parent compounds of the high temperature superconductors.

Often when speaking of "metals" vs. "insulators", we are interested in the ground state of the material, the state that would describe the material in equilibrium as T approaches 0. Materials with an electrical resistivity that tends toward infinity as T approaches 0 are insulators in this sense.

Quantum dots in graphene

The progress in graphene experiments continues. Unsurprisingly, many people are interested in using graphene, a natural 2d electronic system, to make what some would call quantum dots: localized puddles of electrons separated from "bulk" leads by tunnel barriers. Step one in making graphene quantum dots is to etch graphene into a narrow constriction. You can end up with localized electronic states due to disorder (from the edges and the underlying substrate). This Nano Letter shows examples of this situation. Alternately, you can make structures using gates that can define local regions of p-type (local chemical potential biased into the valence band) and n-type (conduction band) conduction, separated by tunnel junctions formed when p and n regions run into each other. That situation is described here. Neat stuff. I would imagine that low temperature transport measurements through such structures in the presence of applied magnetic fields should be very revealing, given the many predictions about exotic magnetic properties in edge states of graphene ribbons.

The new science and technology team

The President-elect has named his science team. Apart from the fact that these folks are all highly qualified (the new administration will have two Nobel laureates advising it directly), I'm told by a senior colleague well-versed in policy that the real good news is the re-promotion of the science advisor position back to the level of authority that it had prior to 2001, and the reinvigoration of PCAST.

At the risk of giving offense....

I see that New Scientist has an article effectively making fun of the Department of Defense for asking their major scientific advisory panel, JASON, to look into a company's claim that it could use gravity waves as an imaging tool. JASON rightly determined that this was not something to worry about. Seems like a non-story to me. Thank goodness New Scientist has never actively promoted something manifestly scientifically wacky on their front cover, like a microwave cavity that violates conservation of momentum. Oh wait.

Outside shot

Since the President-Elect has not yet named his science advisor (though his transition team has named point people, and the nominee for Secretary of Energy has impeccable credentials), I thought I'd point out another crucial way that I would fit in. Sure, I'm under 5' 8" tall, but I can (sometimes) shoot; as some of my college friends can attest, I won a gift certificate in undergrad days by sinking a shot from the top of the key at a women's basketball game halftime promo. (For the humor-impaired: I'm not really in the running to be part of the Obama administration.)

Let them fail.

Please explain to me why we should give AIG another penny.

A couple of ACS papers

Two recent papers in the ASAP section of Nano Letters caught my eye.

The first is van der Molen et al., "Light-controlled conductance switching of ordered metal−molecule−metal devices". I've written a blurb about this for the ACS that will eventually show up here. The Schönenberger group has been working for a while on an approach for measuring molecular conductances that is based on networks of metal nanoparticles linked by molecules of interest. The idea is to take metal nanoparticles and form an ordered array of them with neighbors linked by molecules of interest covalently bound to the particle surfaces. The conductance of the array tells you something about the conductance of the particle-molecule-particle junctions. This is simple in concept and extremely challenging in execution, in part because when the metal nanoparticles are made by chemical means they are already coated with some kind of surfactant molecules to keep them suspended in solution. Performing the linking chemistry in a nice way and ending up with an ordered array of particles rather than a blob of goo requires skill and expertise. These folks have now made arrays incorporating molecules that can change reversibly change their structure upon exposure to light of the appropriate wavelength. The structural changes show up in photo-driven changes in the array conductance.

The second is Ryu et al., "CMOS-Analogous Wafer-Scale Nanotube-on-Insulator Approach for Submicrometer Devices and Integrated Circuits Using Aligned Nanotubes". Lots of people talk a good game about trying to make large-scale integrated circuits using nanotubes, but only a couple of groups have made serious progress. This paper by Chongwu Zhou's group shows that they can take arrays of tubes (grown by chemical vapor deposition on quartz or sapphire substrates), transfer them to Si wafers via a clever method involving gold, pattern the tubes, put down electrodes for devices, burn out the metallic tubes, and dope the semiconductor tubes chemically to do either p or n-type conduction. They are also working on fault-tolerant architectures to deal with the fact that each transistor (which in this case incorporates an ensemble of tubes) has slightly different characteristics.

Manhattan and Apollo project metaphors

Relatively regularly these days there are calls for a Manhattan or Apollo style project to address our energy challenges. While this may sound good, it's worth considering what such a project would actually mean. I found this article (pdf) to be helpful. For the Manhattan project, peak annual funding reached about 1% of total federal outlays and 0.4% of GDP. For Apollo, the peak annual numbers were 2.2% of the federal budget and also 0.4% of GDP. What would that mean in today's numbers? Well, the federal budget is on the order of $3T, and the GDP is around $14T. If we use the GDP numbers, such a commitment of resources would be $56B. That's approximately the combined budgets of DOE, NIH, and NSF. Bear in mind that when we did Apollo, it's not like all other efforts stopped, so really pulling something like this off would require a significant allotment of money.

It's worth pointing out that the government has given three times this amount to AIG alone. It's also worth mentioning that communications technologies are vastly superior to those of the past. Presumably large collaborations can be managed more easily and would eliminate the need to uproot the top researchers in the world from their homes and relocate them in a single central location.

Anyway, those are at least some real numbers, and they're not crazy or unattainable given a strong lead in national priorities from the top. The real challenge is figuring out what the true goal is. It's fine to say "energy independence" or some target number for renewables, but the global energy challenge is a lot more diffuse and multidimensional than either putting people on the moon or developing the atomic bomb.

Overkill

I know that the journal is called Nano Letters, but using the "nano" prefix three times in the title of a paper is a little extreme.

Energy.

As US readers have probably heard by now, Steve Chu has been selected by President-Elect Obama to be the new Secretary of Energy. I think that this is very good news. He's extremely smart, and he's been involved in pretty much the entire research enterprise, from his days at Bell Labs to running a research group at Stanford to serving as department chair to acting as director at LBL. He's been actively worrying about both basic and applied research and understands the actual energy demands of the country and the world. As the finance folks say, past performance is not necessarily indicative of future results, but this appointment gives me real cause for optimism. Steve Chu is extremely qualified for this.

What to do about public perception of science

From the comments on my last post, it's clear that there are some number of science types out there who view the situation as hopeless: the public is poorly informed and his bigger things to worry about; despite having direct evidence every day of the importance of science (ubiquitous computers, lasers, GPS, MRI, DNA testing) the public feels that science is somehow not relevant to their lives and finds even the basic concepts inaccessible; because there is no financial incentive for people to learn about science they won't; etc. While there is a grain of truth to these comments, there is plenty of evidence that is more hopeful. There is no question that certain science topics capture the public imagination: Mars rovers, using genetic technology to cure diseases or identify relationships between individuals or species, the LHC (talk about an effective marketing job, at least to some segment of the population).

Chad Orzel has many good things to say about what scientists can do to help improve the situation, and I won't repeat them here. If you are personally trying to do outreach, I do have one suggestion. Remember that people like a compelling story and interesting characters. The story can be a scientific one (Longitude), a personal one (Genius), or a large-scale drama (The Making of the Atomic Bomb), but it is possible to capture and hold people's attention on scientific subjects. I'm not suggesting that everyone should go out and try to write a popular book on science, but try to remember what makes the best of those books successful.