I'll bet that this looks good to the NSF as outreach....

Here is a neat little video of Prof. Jim Kakalios, who acted as a science advisor on the forthcoming Watchmen movie. Watchmen is a graphic novel by Allen Moore, set in a dystopian alternate 1985, in a world where there really are "costumed vigilantes". The story looks at what kind of people would dress up in costumes and fight crime (answer: damaged people), and what it would do to society if there really was a single being (who happens to be American) with godlike superpowers.

Anyway, it sounds like Prof. Kakalios had a great time, and helped the movie producers get certain things to look right (e.g., a 1959 physics lab; a 1985 physics lab; equations on chalkboards in the background). This sort of thing seems like it would be great fun. So, to all you Hollywood producers out there, call me :-)

This week in cond-mat

I know that it's been a while since I've done one of these. It's not because of a lack of interesting papers on the arxiv; rather, it's been entirely due to my own lack of time. On to a couple of interesting papers from this week....

arxiv:0902.3014 - Miroschnichenko et al., Fano resonance in nanoscale structures
This is an article intended for Reviews of Modern Physics that takes pedagogical, unifying look at Fano resonances, particularly in nanostructures. (I've linked to the version with high-res figures.) A Fano resonance is a particular kind of (in general) asymmetric resonance lineshape that results from interference between, for example, [direct transmission into a continuum of states] and [transmission involving scattering from a resonant level]. The end result is a resonance lineshape that can look like resonant transmission, resonant absorption, and a variety of asymmetric shapes in between. Originally proposed by Ugo Fano to explain phenomena in atomic physics, Fano resonances are all over the place in nanoscale systems. This paper actually gives about as nice a pedagogical description of this physics as you're going to find.

arxiv:0902.3305 - Deshpande et al., Spatially-resolved temperature measurements of electrically heated carbon nanotubes
A major issue in nanoscale electronic transport experiments is the question of dissipation and energy relaxation. By applying a voltage across a nanostructure in a measurement of conduction, one is driving the electronic distribution (which electronic states are occupied as a function of energy or momentum) out of thermal equilibrium. Eventually, the electrons rethermalize, transferring their energy to one another and to the vibrational modes of the material in question. How this happens in detail can be quite complicated, and nonthermal distributions of electrons and vibrations can exist over relatively long distance scales (say hundreds of nanometers at low temperatures). These folks have been able to use scanning Raman microscopy to map out the local lattice temperature of carbon nanotubes as current is passed through them. In this case they are looking at the shift of a particular nanotube vibrational mode, and using that as an effective thermometer. It's a pretty experiment that demonstrates how much we can learn by combining electronic measurements with complementary techniques.

Nice animation re: the credit crisis

I just saw this (link to video), and I was quite impressed. Mr. Jarvis (the animator) has a real pedagogical gift. I wonder if one could make videos this cleanly done about CM physics....

What is a phonon?

In hindsight, I suppose that I should have addressed phonons earlier. A phonon is a quantized sound wave - a collective vibrational mode of a solid (or liquid). In a crystalline solid, the idea is that the atoms in the solid are displaced, at any given instant, from their equilibrium positions. For a single phonon, the instantaneous displacements are periodic in space (that is, there is some wavelength, where atoms separated by an integer number of wavelengths are displaced the same amount). The displaced atoms feel restoring forces due to their interactions with neighbors, and will tend to oscillate in time around their equilibrium positions. When the wavelength is much longer than the interparticle separation, the frequency of those oscillations times the wavelength gives the speed of sound for the material - phonons propagate along at the speed of sound. In general, the speed of sound can depend on the direction of propagation as well as the direction of the direction of the displacement. If the displacement is along the direction of propagation, the sound is longitudinal; if the displacement is normal to the direction of propagation, the sound is transverse.

The quantum nature of phonons comes in when one discusses their energy content. In a classical mechanical oscillator, you can dump in as much energy as you want; the energy content is proportional to the square of the amplitude of the oscillation, and that can be varied continuously. In a quantum mechanical oscillator of frequency f, the energy content of that oscillator can only take on discrete values, (n + 1/2)hf, where n is a nonnegative integer. This is a subtle yet hugely important distinction. Mathematically it explains a major contribution to the heat capacity of crystalline solids at low temperatures (and it's very strongly related to the form of blackbody radiation when one is worrying about photons rather than phonons).

Because they have a wavelength and therefore a wavevector (and an effective momentum) as well as an energy, one can think about processes that involve the emission, propagation, and scattering of phonons - they have particle-like attributes in that sense.

(For a layperson discussion, I'm avoiding subtle distinctions like acoustic vs. optical phonons. If you really care, in acoustic phonons all the atoms within a unit cell move together, while for optical phonons different atoms within a single unit cell move by different amounts.)

No, it's not a nanorobot.

Once again, nano-hype. This time the subject is this very nice paper from Seeman's group at NYU, in which they use DNA-based tools to perform programmed self-assembly of some cute nanostructures (also made out of DNA). Seeman has been doing pioneering work for years on leveraging the great specificity of DNA chemistry to make interesting nanostructures. The trick is that each nucleic acid base in DNA likes to hydrogen bond with its own particular complementary base. This specificity of binding plays an essential role in eukaryotic biology, and we now know how to engineer it. In this case, Seeman and coauthors set up a situation where user-defined shapes made from DNA (created using "DNA origami") are bound in specific places and not elsewhere. The major innovation is that they've figured out a way to implement a form of error correction, and in principle they can alter the assembly parameters (that is, which peg goes into which hole) on the fly.

This is nice work, but it's not a nanorobot, not by any reasonable definition of the term. Sorry. By the way, the word "robot" doesn't appear anywhere in the paper (except in the title to one of the references).

What is a plasmon?

Continuing my series of posts trying to describe condensed matter topics in relatively non-technical language....

As I've mentioned before, in condensed matter physics, we tend to give particle-like names (that is, ones that end in "-on") to excitations of systems that have well-defined particle-like attributes, like momentum, energy, and angular momentum (such as spin). Plasmons are another example of this, and lately they've become extremely fashionable because it's increasingly clear that they can be technologically useful.

A plasmon is a collective excitation of the electronic "fluid" in a piece of conducting material, like ripples on the surface of a pond are a collective mode of the water molecules of the liquid. The simile here isn't too far off, because like water, the electronic fluid in a metal is pretty close to incompressible. If you push down on the surface of a pond somewhere with a float, the density of the water doesn't change; instead the water elsewhere is displaced, because the water molecules have finite volume and push each other out of the way. The electronic fluid acts similarly, not because of any finite size or even the Coulomb repulsion of the electrons, but mostly because of the Pauli exclusion principle, which tends to keep the electrons out of each others' way.

These electronic ripples can have a well-defined wavelength (which quantum mechanics tells us is related to their momentum). What makes them have a frequency? That is, what makes the plasmon waves wave? When the electrons are displaced, the positive charge left behind exerts an attractive force on the electrons, trying to pull them back to their original positions. This interaction is what makes the plasmons oscillate once they're excited, and these Coulomb interactions are also why plasmons cost energy to excite. These Coulomb interactions with the positive background charge also force plasmons to obey certain boundary conditions at the edges of the host metal. As a result, nanoparticles can have discrete allowed plasmonic modes strongly influenced by particle shape, while larger structures (e.g., thin metal films) can have propagating plasmon modes over a broad range of wavelengths. Typical plasmon frequencies are comparable to the frequencies of visible light (i.e., ~ 10¹⁵ Hz). Plasmons decay (into incoherent electron-hole pair excitations), eventually dissipating their energy as the sloshing electrons scatter instead of oscillating smoothly, and as oscillating electric dipoles (and other multipoles) radiate.

Plasmons have gotten so much attention lately for several reasons. They may offer a way of shuttling information around on computer chips that naturally interfaces with optics. Plasmons are also associated with large local electric fields at metal surfaces, which can be very useful for certain kinds of spectroscopies and things like optical trapping. Finally, in properly designed materials, plasmon properties can be manipulated so that the overall optical response of a conducting system can be tuned, leading to lots of hope and hype about "perfect lenses" and "invisibility cloaks".

Whew, again.

Thankfully, my bad feeling was off-base. According to Speaker Pelosi's summary of the conference committee version of the stimulus (word document here), the NSF will end up with $3B, DOE Office of Science gets $1.6B, there will be an ARPA-E with $400M, NIST will get $580M, NIH will get $8.5B (more than the entire NSF annual budget, by a good fraction) for research and an additional $1.5B for university facilities; and NASA will get $1B, with $400M of that targeted for climate research.

Now all they have to do is actually pass this thing.

I know that many people out there have philosophical objections to this kind of investment being done in a stimulus bill (as opposed to a regular appropriation). I also know that big one-time spikes in funding can be disruptive and harmful in the long term. Still, this is the first decent investment in the physical sciences in years, and it's hard for me to feel misgivings about it given that we've given more than TEN TIMES the total up there in taxpayer dollars to prop up just AIG.

I've got a bad feeling about this....

...but I'm prepared to be surprised. For some reason my gut is telling me that the House/Senate conference is going to eviscerate all the science funding in the stimulus except NIH. I hope I'm wrong. I guess we'll find out in a few hours. I'd feel better about this whole business if Grassley wasn't on the conference.

Experimental physics rules to live by?

I thought that it might be fun to have a discussion about "rules to live by" in experimental physics. Here are a few that I think may qualify, and of course I'd appreciate your suggestions for others....

• Know your apparatus. Don't blindly use a piece of equipment as a black box. Understand how it works. Just because some hand-me-down voltage supply is supposed to put out a square wave doesn't mean that it actually does. You can't blindly use a 10 MOhm input impedance voltage amplifier to measure the voltage dropped across a 1 GOhm load.
  
• When trying to understand something new, turn every experimental knob as much as you can. You'll be kicking yourself if you decide not to bother cooling the sample below 10 K, and then someone else finds an exciting effect at 9 K. Clearly one needs to strike a balance between time and likelihood of discovery, but in general, if you can tune a parameter, do so.
• Estimate the expected signal size, in real, useful units. Double-check your calculation. My thesis advisor used to tell a story about some students in an advanced undergrad lab who thought their experiment was working well, but it turns out that a wire was actually disconnected, and they'd screwed up the calculation of expected signal size so that the answer agreed with the output of the broken setup.
• Turn knobs finely enough. There are multiple tales out there in physics of discoveries being missed or almost missed because someone was tuning some parameter in coarse steps and skipped over a big feature in the data. That's how superconductivity in MgB₂ was missed back in the 1960's, and how SLAC almost didn't co-discover the J/Psi particle.
• Yes, you really do need to reproduce that result. You can see anything once. If the wild, exciting effect you just observed is real, you should be able to see it again if you're careful and diligent.
• Be your own harshest critic. If you won't, the referees surely will.
  

AAAAAAAGGGH!

I just don't believe it. The "moderate" senators trying to whittle down the stimulus package to avoid a filibuster in the Senate really are suggesting that NSF funding be cut, presumably b/c of the silly porn-viewing incident.

UPDATE: Whew. Thanks in part to hard lobbying by a large number of scientists and engineers, especially the folks at Sciencedebate 2008, the Senate compromise version of the stimulus package was not eviscerated of support for science. It is interesting to note, though, that the NIH will get a boost that exceeds the NSF's entire budget.

To tide you over....

Proposal deadlines are almost done with, and then I'll try to post more. In the meantime, here's a question to tide you over. Superconductors are classified as "type I" or "type II". In type I superconductors, superconductivity is completely destroyed above some critical externally applied magnetic field, H_c. To be more jargon-y, in these materials the coherence length (the typical spatial extent of pair-like correlations between electrons in the superconductor) is much larger than the magnetic penetration depth (the distance that a magnetic field penetrates into a superconductor before it is screened away by circulating supercurrents). In type II superconductors, above a critical field H_c,1 magnetic flux starts to penetrate the superconductor in the form of vortices (localized regions with nonsuperconducting cores through which magnetic flux is threaded, and around which are circulating supercurrents). Above a second, higher critical field, H_c,2, superconductivity is eventually destroyed. In type II superconductors, the coherence length is much shorter than the penetration depth.

So here's the question: why are almost all the pure elemental superconductors type I, and why are essentially all alloys type II? Is there a simple argument that explains this? If there is, I haven't heard it....

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....