When freshman physics models fail

When we teach basic ac circuits in second semester freshman physics, or for that matter in intro to electrical engineering, we introduce the idea of an impedance, \(Z\), so that we can make ac circuit problems look like a generalization of Ohm's law.  For dc currents, we say that \(V = I R\), the voltage dropped across a resistor is linearly proportional to the current.  For reactive circuit elements and ac currents, we use complex numbers to keep track of phase shifts between the current and voltage.  Calling \(j \equiv \sqrt{-1}\), we assume that the ac current has a time dependence \(\exp(-j \omega t\).  Then we can say that the impedance \(Z\) of an inductor is \(j \omega L\), and write \(V = Z I\) for the case of an ac voltage across the inductor.

Where does that come from, though?  Well, it's really Faraday's law.  The magnetic flux through an inductor is given by \(\Phi = LI\).  We know that the voltage induced between the ends of such a coil is given by \(-d\Phi/dt = L (dI/dt) + (dL/dt) I\), and in an ordinary inductor, \(dL/dt\) is simply zero.  But not always!

Last fall and into the spring, two undergrads in my lab (aided by two grad students) were doing some measurements of inductors filled with vanadium dioxide powder, a material that goes through a sharp first-order phase transition at about 65 \(^{\circ}\)C from a low temperature insulator to a high temperature poor metal.  At the transition, there is also a change in the magnetic susceptibility of the material.  What I rather expected to see was a step-like change in the inductive response going across the transition, and an accompanying step-like change in the loss (due to resistive heating in the metal).  Both of these effects should be small (just at the edge of detection in our scheme).  Instead, the students found something very different - a big peak in the lossy response on warming, and an accompanying dip in the lossy response on cooling.  We stared at this data for weeks, and I asked them to run a whole variety of checks and control experiments to make sure we didn't have something wrong with the setup.  We also found that if we held the temperature fixed in the middle of the peak/dip, the response would drop off to what you'd expect in the absence of any peak/dip.   No, this was clearly a real effect, requiring a time-varying temperature to be apparent, and eventually it dawned on me what was going on:  we were seeing the other contribution to \(d\Phi/dt\)!  As each grain flicks into the new phase, it makes a nearly singular contribution to \(dL/dt\) because the transition for each grain is so rapid.

This is analogous to the Barkhausen effect, where a pickup coil wrapped around a piece of, e.g., iron and wired into speakers produces pops and crackling sounds as an external magnetic field is swept.  In the Barkhausen case, individual magnetic domains reorient or domain walls propagate suddenly, also giving a big \(d\Phi/dt\).  In our version, temperature is causing sudden changes in susceptibility, but it's the same basic idea.

This was great fun to figure out, and I really enjoy that it shows how the simple model of the impedance of an inductor can fail dramatically if the material in the coil does interesting things.  The paper is available here.

What is a "bad metal"? What is a "strange metal"?

Way back in the mists of time, I wrote about what what physicists mean when they say that some material is a metal.  In brief, a metal is a material that has an electrical resistivity that decreases with decreasing temperature, and in bulk has low energy excitations of the electron system down to arbitrarily low energies (no energy gap in the spectrum).  In a conventional or good metal, it makes sense to think about the electrons in terms of a classical picture often called the Drude model or a semiclassical (more quantum mechanical) picture called the Sommerfeld model.  In the former, you can think of the electrons as a gas, with the idea that the electrons travel some typical distance scale, \(\ell\), the mean free path, between scattering events that randomize the direction of the electron motion.  In the latter, you can think of a typical electronic state as a plane-wave-like object with some characteristic wavelength (of the highest occupied state) \(\lambda_{\mathrm{F}}\) that propagates effortlessly through the lattice, until it comes to a defect (break in the lattice symmetry) causing it to scatter.  In a good metal, \(\ell >> \lambda_{\mathrm{F}}\), or equivalently \( (2\pi/\lambda_{\mathrm{F}})\ell >> 1\).  Electrons propagate many wavelengths between scattering events.  Moreover, it also follows (given how many valence electrons come from each atom in the lattice) that \(\ell >> a\), where \(a\) is the lattice constant, the atomic-scale distance between adjacent atoms.

Another property of a conventional metal:  At low temperatures, the temperature-dependent part of the resistivity is dominated by electron-electron scattering, which in turn is limited by the number of empty electronic states that are accessible (e.g., not already filled and this forbidden as final states due to the Pauli principle).    The number of excited electrons (that in a conventional metal called a Fermi liquid act roughly like ordinary electrons, with charge \(-e\) and spin 1/2) is proportional to \(T\), and therefore the number of empty states available at low energies as "targets" for scattering is also proportional to \(T\), leading to a temperature-varying contribution to the resistivity proportional to \(T^{2}\).

A bad metal is one in which some or all of these assumptions fail, empirically.  That is, a bad metal has gapless excitations, but if you analyze its electrical properties and tried to model them conventionally, you might find that the \(\ell\) that you infer from the data might be small compared to a lattice spacing.   This is called violating the Ioffe-Mott-Regel limit, and can happen in metals like rutile VO₂ or LaSrCuO₄ at high temperatures.

A strange metal is a more specific term.  In a variety of systems, instead of having the resistivity scale like \(T^{2}\) at low temperatures, the resistivity scales like \(T\).  This happens in the copper oxide superconductors near optimal doping.  This happens in the related ruthenium oxides.  This happens in some heavy fermion metals right in the "quantum critical" regime.  This happens in some of the iron pnictide superconductors.  In some of these materials, when some technique like photoemission is applied, instead of finding ordinary electron-like quasiparticles, a big, smeared out "incoherent" signal is detected.  The idea is that in these systems there are not well-defined (in the sense of long-lived) electron-like quasiparticles, and these systems are not Fermi liquids.

There are many open questions remaining - what is the best way to think about such systems?  If an electron is injected from a boring metal into one of these, does it "fractionalize", in the sense of producing a huge number of complicated many-body excitations of the strange metal?  Are all strange metals the same deep down?  Can one really connect these systems with quantum gravity?  Fun stuff.

What is the Casimir effect?

This is another in an occasional series of posts where I try to explain some physical phenomena and concepts in a comparatively accessible way.  I'm going to try hard to lean toward a lay audience here, with the very real possibility that this will fail.

You may have heard of the Casimir effect, or the Casimir force - it's usually presented in language that refers to "quantum fluctuations of the electromagnetic field", and phrases like "zero point energy" waft around.  The traditional idea is that two electrically neutral, perfectly conducting plates, parallel to each other, will experience an attractive force per unit area given by \( \hbar c \pi^{2}/(240 a^{4})\), where \(a \) is the distance between the plates.  For realistic conductors (and even dielectrics) it is possible to derive analogous expressions.  For a recent, serious scientific review, see here (though I think it's behind a paywall).

To get some sense of where these forces come from, we need to think about van der Waals forces.  It turns out that there is an attractive force between neutral atoms, say helium atoms for simplicity.  We are taught to think about the electrons in helium as "looking" like puffy, spherical clouds - that's one way to visualize the electron's quantum wave function, related to the probability of finding the electron in a given spot if you decided to look through some experimental means.  If you imagine using some scattering experiment to "take a snapshot" of the helium atom, you'd find the two electrons located at particular locations, probably away from the nucleus.  In that sense, the helium atom would have an "instantaneous electric dipole moment".  To use an analogy with magnetic dipoles, imagine that there are little bar magnets pointing from the nucleus to each electron.  The influence (electric field in the real atom; magnetic field from the bar magnet analogy) of those dipoles drops off in distance like \(1/r^{3}\).  Now, if there was a second nearby atom, its electrons would experience the fields from the first atom.  This would tend to influence its own dipole (in the magnet analogy, instead of the bar magnets pointing on average in all directions, they would tend to align with the field from the first atom, rather like how a compass needle is influenced by a nearby bar magnet).   The result would be an attractive force, proportional to \(1/r^{6}\).

In this description, we ignored that it takes time for the fields from the first atom to propagate to the second atom.  This is called retardation, and it's one key difference between the van der Waals interaction (when retardation is basically assumed to be unimportant) and so-called Casimir-Polder forces.   

Now we can ask, what about having more than two atoms?  What happens to the forces then?  Is it enough just to think of them as a bunch of pairs and add up the contributions?  The short answer is, no, you can't just think about pair-wise interactions (interference effects and retardation make it necessary to treat extended objects carefully).

What about exotic quantum vacuum fluctuations, you might ask.  Well, in some sense, you can think about those fluctuations and interactions with them as helping to set the randomized flipping dipole orientations in the first place, though that's not necessary.  It has been shown that you can do full, relativistic, retarded calculations of these fluctuating dipole effects and you can reproduce the Casimir results (and with greater generality) without saying much of anything about zero point stuff.  That is why while it is fun to speculate about zero point energy and so forth (see here for an entertaining and informative article - again, sorry about the paywall), there really doesn't seem to be any way to get net energy "out of the vacuum".

Two cool papers on the arxiv

The beginning of the semester is a crazy time, so blogging is a little light right now.  Still, here are a couple of recent papers from the arxiv that struck my fancy.

arxiv:1408.4831 - "Self-replicating cracks:  A collaborative fracture mode in thin films," by Marthelot et al. 
This is very cool classical physics.  In thin, brittle films moderately adhering to a substrate, there can be a competition between the stresses involved with crack propagation and the stresses involved with delamination of the film.  The result can be very pretty pattern formation and impressively rich behavior.  A side note:  All cracks are really nanoscale phenomena - the actual breaking of bonds at the tip of the propagating crack is firmly in the nano regime.

arxiv:1408.6496 - "Non-equilibrium probing of two-level charge fluctuators using the step response of a single electron transistor," by Pourkabirian et al. 

I've written previously (wow, I've been blogging a while) about "two-level systems", the local dynamic degrees of freedom that are ubiquitous in disordered materials.  These little fluctuators have a statistically broad distribution of level asymmetries and tunneling times.  As a result, when perturbed, the ensemble of these TLSs responds not with a simple exponential decay (as would a system with a single characteristic time scale).  Instead, the TLS ensemble leads to a decaying response that is logarithmic in time.  For my PhD I studied such (agonizingly) slow relaxations in the dielectric response and acoustic response of glasses (like SiO2) at cryogenic temperatures.   Here, the authors use the incredible charge sensitivity of a single-electron transistor (SET) to look at the relaxation of the local charge environment near such disordered dielectrics.  The TLSs often have electric dipole moments, so their relaxation changes the local electrostatic potential near the SET. Guess what:  logarithmic relaxations.  Cute, and brings back memories of loooooong experiments from grad school.

Science and engineering research infrastructure - quo vadis?

I've returned from the NSF's workshop regarding the successor program to the NNIN.  While there, I learned a few interesting things, and I want to point out a serious issue facing science and engineering education and research (at least in the US).

• The NNIN has been (since 2010) essentially level-funded at $16M/yr for the whole program, and there are no indications that this will change in the foreseeable future.  (Inflation erodes the value of that sum as well over time.)  The NNIN serves approximately 6000 users per year (with turnover of about 2200 users/yr).  For perspective, a truly cutting edge transmission electron microscope, one instrument, costs about $8M.  The idea that the NNIN program can directly create bleeding edge shared research hardware across the nation is misguided.
• For comparison, the US DOE has five nano centers.  The typical budget for each one is about $20M/yr.  Each nano center can handle around 450 users/yr.  Note that these nano centers are very different things than NNIN sites - they do not charge user fees, and they are co-located with some truly unique characterization facilities (synchrotrons, neutron sources).  Still, the DOE is spending seventeen times as much per user per year in their program as the NNIN.
• Even the DOE, with their much larger investment, doesn't really know how to handle "recapitalization".  That is, there was money available to buy cutting edge tools to set up their centers initially, but there is no clear, sustainable financial path to be able to replace aging instrumentation.  This is exactly the same problem faced by essentially every research university in the US.  Welcome to the party.  
• Along those lines:  As far as I can tell (and please correct me if I'm wrong about this!), every US federal granting program intended to have a component associated with increasing shared research infrastructure at universities (this includes the NSF MRI program, MRSEC, STC, ERC, CCI; DOE instrumentation grants, DOE centers like EFRCs, DOD equipment programs like DURIPs) is either level-funded or facing declining funding levels.  Programs like these often favor acquisition of new, unusual tools over standard "bread-and-butter" as well.  Universities are going to have to rely increasingly on internal investment to acquire/replace instrumentation.  Given that there is already considerable resentment/concern about perceived stratification of research universities into "haves" and "have-nots", it's hard to see how this is going to get much better any time soon.
• To potential donors who are really interested in the problem of graduate (and advanced undergrad) science and engineering hands-on education:  PLEASE consider this situation.  A consortium of donors who raised, say, $300M in an endowment could support the equivalent of the NNIN on the investment returns for decades to come.  This can have an impact on thousands of students/postdocs per year, for years at a time.  The idea that this is something of a return to the medieval system of rich patrons supporting the sciences is distressing.  However, given the constraints of government finances and the enormous sums of money out there in the hands of some brilliant, tech-savvy people who appreciate the importance of an educated workforce, I hope someone will take this possibility seriously.  To put this in further perspective:  I heard on the radio yesterday that the college athletics complex being built at Texas A&M University costs $400M.  Think about that.  A university athletic booster organization was able to raise that kind of money for something as narrowly focused (sorry, Aggies, but you know it's true). 

Distinguishable from magic?

Arthur C. Clarke's most famous epigram is that "Any sufficiently advanced technology is indistinguishable from magic."  A question that I've heard debated in recent years is, have we gone far enough down that road that it's adversely affecting the science and engineering education pipeline?  There was a time when young people interested in technology could rip things apart and actually get a moderately good sense of how those gadgets worked.  This learning-through-disassembly approach is still encouraged, but the scope is much more limited. 

For example, when I was a kid (back in the dim mists of time known as the 1970s and early 80s), I ripped apart transistor radios and at least one old, busted TV.  Inside the radios, I saw how the AM tuner worked by sliding a metal contact along a wire solenoid - I learned later that this was tuning an inductor-capacitor resonator, and that the then-mysterious diodes in there (the only parts on the circuit board with some kind of polarity stamped on them, aside from the electrolytic capacitors on the power supply side) somehow were important at getting the signal out.  Inside the TV, I saw that there was a whopping big transformer, some electromagnets, and that the screen was actually the front face of a big (13 inch diagonal!) vacuum tube.  My dad explained to me that the electromagnets helped raster an electron beam back and forth in there, which smacked on phosphors on the inside of the screen.  Putting a big permanent magnet up against the front of a screen distorted the picture and warped the colors in a cool way that depended strongly on the distance between the magnet and the screen, and on the magnet's orientation, thanks to the magnet screwing with the electron beam's trajectory. 

Now, a kid opening up an ipod or little portable radio will find undocumented integrated circuits that do the digital tuning.  Flat screen LCD TVs are also much more black-box-like (though the light source is obvious), again containing lots of integrated circuits.  Touch screens, the accelerometers that determine which way to orient the image on a cell phone's screen, the chip that actually takes the pictures in a cell phone camera - all of these seem almost magical, and they are either packaged monolithically (and inscrutably), or all the really cool bits are too small to see without a high-power optical microscope.  Even automobiles are harder to figure out, with lots of sensors, solid-state electronics, and an architecture that often actively hampers investigation. 

I fully realize that I'm verging on sounding like a grumpy old man with an onion on his belt (non-US readers: see transcript here).  Still, the fact that understanding of everyday technology is becoming increasingly inaccessible, disconnected with common sense and daily experience, does seem like a cause for concern.  Chemistry sets, electronics sets, arduinos and raspberry pi-s, these are all ways to fight this trend, and their use should be encouraged!

Some quick cool science links

Here are a few neat things that have cropped up recently:

• The New Horizons spacecraft is finally getting close enough to Pluto to be able to image Pluto and Charon orbiting about their common (approximate, b/c of other moons) center of mass.
• The Moore Foundation announced the awardees in the materials synthesis component of their big program titled Emergent Phenomena in Quantum Systems.  Congratulations all around.  
• Here's a shock:  congressmen in the pockets of the United Launch Alliance don't like SpaceX.
• Cute toy.
• The Fields Medal finally goes to a woman, Maryam Mirzakhani.  Also getting a share, Manjul Bhargava, who gave the single clearest math talk I've ever seen, using only a blank transparency and a felt-tip pen.

Nanotubes by design

There is a paper in this week's issue of Nature (with an accompanying news commentary by my colleague Jim Tour) in which the authors appear to have solved a major, two decade+ challenge, growing single-walled carbon nanotubes of a specific type.   For a general audience:  You can imagine rolling up a single graphene sheet and joining the edges to make a cylinder.  There are many different ways to do this.  The issue is, different ways of rolling up the sheet lead to different electronic properties, and the energetic differences between these different tube types are very small.  When people have tried to grow nanotubes by any number of methods, they tend to end up with a bunch of tube types of similar diameters, rather than just the one they want.

The authors of this new paper have taken an approach that has great visual appeal.  They have used synthetic chemistry to make a planar hydrocarbon molecule that looks like they've taken the geodesic hemisphere end-cap of their desired tube and cut it to lay it flat - like making a funky projection to create a flat map of a globe.  When placed on a catalytically active Pt surface at elevated temperatures, this molecular seed can fold up into an endcap and start growing as a nanotube.  The authors show Raman spectroscopic evidence that they only produce the desired tube type (in this case, a metallic nanotube).  The picture is nice, and the authors imply that they could do this for other desired tube types.  It's not clear whether this is scalable for large volumes, but it's certainly encouraging.

This is very cute.  People in the nanotube game have been trying to do selective synthesis for twenty years.  Earlier this summer, a competing group showed progress in this direction using nanoparticle seeds, an approach pursued by many over the years with limited success.  It will be fun to see where this goes.  This is a good example of how long it can take to solve some materials problems.

Does being a physicist ruin science fiction for me? Generally, no.

For the past few years, as I've been teaching honors freshman mechanics, I've tried to work in at least one homework problem based on a popular sci-fi movie.  Broadening that definition to include the Marvel Cinematic Universe, I've done Iron Man, Captain America, the Avengers.  Yesterday I saw Guardians of the Galaxy, and I've got a problem in mind already.

I've been asked before, does being a physicist just ruin science fiction books and movies for me?  Does bad physics in movies or sci-fi books annoy me since I can't not see it?  Generally, the answer is "no".  I don't expect Star Trek or Star Wars to be a documentary, and I completely understand why bending physics rules can make a story more fun.  Iron Man would be a lot less entertaining if Tony Stark couldn't build an arc reactor with enough storage capacity and power density to fly long distances.  Trips through outer space that require years of narrative time just to get to Jupiter are less fun than superluminal travel.  If anything, I think well-done science fiction can be creatively inspiring.

One thing that does bug me is internally inconsistent bad physics or bad science.  For example, in the book Prey by Michael Crichton, it's established early on that any tiny breach in a window, etc. is enough for the malevolent nanocritters to get in, yet at the climax of the book the author miraculously forgets this (because if he'd remembered it the protagonist would've died).  Another thing that gets me is trivially avoidable science mistakes.  For example, in a Star Trek:TNG episode (I looked it up - it was this one), they quote a surface temperature less than absolute zero.  I'm happy to serve as a Hollywood science advisor to avoid these problems :-)

A book, + NNIN

Sorry for the posting drought.  There is a good reason:  I'm in the final stages of a textbook based on courses I developed about nanostructures and nanotechnology.  It's been an embarrassingly long time in the making, but I'm finally to the index-plus-final-touches stage.  I'll say more when it's in to the publisher.

One other thing:  I'm going to a 1.5 day workshop at NSF in three weeks about the next steps regarding the NNIN.  I've been given copies of the feedback that NSF received in their request for comment period, but if you have additional opinions or information that you'd like aired there, please let me know, either in the comments or via email.

My Nerd Nite talk - video

I mentioned back in February that I'd had the chance to speak at Nerd Nite Houston (facebook link - it's updated more frequently than the website).  It was a blast, and I encourage people in the area to check it out on the last Thursday of each month, location announced on the page, though so far they've all been at Notsuoh. 

Thanks to the fantastic videographic efforts of Jon Martensen, the video of my talk is now available on youtube here.  The talk is about 20 minutes and the rest is the audience Q&A.   All in all, a very fun experience - thanks again to Amado Guloy and the rest of the Nerd Nite folks for giving me the opportunity.

Interesting links: peer review, falsifiability

Slow blogging - I've got the usual papers plus working on finishing a really big writing project (more about that soon), combined w/ summer travel.  The posting rate will pick up again in another week and a half.  In the meantime, here are a few interesting links from the last couple of weeks.

• A thoroughly dishonest scientist (and I guess a couple of other people) were exposed as running an awful peer review scam.  More about this here.  The scam involved creating fake email addresses and identities to mask people essentially reviewing their own and friends' papers.  The worst thing about this whole mess is that it gives ammunition to the anti-science crowd who are convinced that scientific research is a corrupt enterprise - people like the person I wrote about here.
• Peter Woit has written an interesting review of a book about string theory and whether the scientific method needs to be revised to deal with "post-emprical" theory verification, whatever that means.  I haven't read the book, but the idea of post-empiricism is pretty sketchy to me.
• Natalie Wolchover has written an article about some fluid droplet experiments that show quantum-like behavior of droplets (e.g., interference-fringe-like distributions, for example).  The physics here is that the droplets are interacting with associated surface waves of an underlying fluid, and the mechanics of those waves self-consistently guides the droplets.  This is similar in spirit to Bohm's ideas about pilot waves as a way of thinking about quantum mechanics.  The authors of the fluid paper are clearly high on this idea.  These are clearly very cool experiments, but it's a huge stretch to say that they should motivate re-thinking our interpretations of quantum mechanics. 

An expression of concern about an expression of concern

There has been a big kerfluffle about Facebook conducting a mass social psychology experiment.  At heart is the issue of informed consent.  By clicking "ok" on a vaguely worded license agreement, did users really give true informed consent to participate in experiments designed to manipulate them?  The study was published in the Proceedings of the National Academy of Sciences here.  Now, in hindsight, PNAS has published an "Expression of Concern" here about whether the study was in compliance with the Common Rule regarding informed consent by human subjects.  The PNAS editors point out that as a privately funded, for-profit corporation not taking federal funding for this work, Facebook isn't technically bound by this constraint.

This is technically correct (the best kind of correct), but doesn't this have frightening implications?  Does this mean that private companies are free to perform experiments on human subjects without asking for informed consent, so long as they don't violate obvious laws like killing people?  Seems like there must be some statutes out there about human experimentation, right?  Perhaps one of my readers knows this issue....

What are universal conductance fluctuations?

Another realization I had at the Gordon Conference:  there are plenty of younger people in condensed matter physics who have never heard about some mesoscopic physics topics.   Presumably those topics are now in that awkward purgatory of being so established that they're "boring" from the research standpoint, but they are beyond what is taught in standard solid state physics classes (i.e., they're not in Ashcroft and Mermin or Kittel).  Here is my attempt to talk at a reasonably popular level about one of these, so-called "Universal Conductance Fluctuations" (UCF).

In physics parlance, sometimes it can be very useful to think about electrons in solids as semiclassical, a kind of middle ground between picturing them as little classical specks whizzing around and visualizing them as fuzzy, entirely wavelike quantum states.  In the semiclassical picture, you can think of the electrons as following particular trajectories, and still keep in mind their wavelike aspect by saying that the particles rack up phase as they propagate along.  In a typical metal like gold or copper, the effective wavelength of the electrons is the Fermi wavelength, \( \lambda_{\mathrm{F}} \sim 0.1~\)nm.  That means that an electron propagating 0.1 nm changes its quantum phase by about \(2 \pi\).  In a relatively "clean" metal, electrons propagate along over long distances, many Fermi wavelengths, before scattering.  At low temperatures, that scattering is mostly from disorder (grain boundaries, vacancies, impurities).

The point of keeping track of the quantum phase \(\phi\) is that this is how we find probabilities for quantum processes.  In quantum mechanics, if there are two paths to do something, with (complex) amplitudes \(A_{1}\) and \(A_{2}\), the probability of that something is \(|A_{1} + A_{2}|^{2}\), which is different than just adding the probabilities of each path, \(|A_{1}|^{2}\) and \(|A_{2}|^{2}\).  For an electron propagating, for each trajectory we can figure out an amplitude that includes the phase.  We add up all the (complex) amplitudes for all the possible trajectories, and then take the (magnitude) square of the sum.  The cross terms are what give quantum interference effects, such as the wavy diffraction pattern in the famous two-slit experiment.  This is how Feynman describes interference in his great little book, QED. 

Electronic conduction in a disordered metal then becomes a quantum interference experiment.  An electron can bounce off various impurities or defects in different sequences, with each trajectory having some phase.  The exact phases are set by the details of the disorder, so while they differ from sample to sample, they are the same within a given sample as long as the disorder doesn't change.  The conduction of the electrons is then something like a speckle pattern.  The typical scale of that speckle is a change in the conductance \(G\) of something like \(\delta G \sim e^{2}/h\).  Note that inelastic processes can change the electronic wavelength (by altering the electron energy and hence the magnitude of its momentum) and also randomize the phase - these "dephasing" effects mean that on length scales large compared to some coherence length \(L_{\phi}\), it doesn't make sense to worry about quantum interference.

Now, anything that alters the relative phases of the different trajectories will lead to fluctuations in the conductance on that scale (within a coherent region).  A magnetic field can do this, because the amount of phase racked up by propagating electrons depends not just on their wavelength (basically their momentum), but also on the vector potential, a funny quantity discussed further here.  So, ramping a magnetic field through a (weakly disordered) metal (at low temperatures) can generate sample-specific, random-looking but reproducible, fluctuations in the conductance on the order of \(e^{2}/h\).  These are the UCF. 

By looking at the UCF (their variation with magnetic field, temperature, gate voltage in a semiconductor, etc.), one can infer \(L_{\phi}\), for example.  These kinds of experiments were all the rage in ordinary metals and semiconductors in the late 1980s and early 1990s.  They enjoyed a resurgence in the late '90s during a controversy about coherence and the fate of quasiparticles as \(T \rightarrow 0\), and are still used as a tool to examine coherence in new systems as they come along (graphene, atomically thin semiconductors, 2d electron gases in oxide heterostructures, etc.). 

Gordon Conference thoughts

Because of travel constraints I'm missing the last day of the meeting, but here are some thoughts, non-science first:

• These meetings remain a great format - not too big, a good mix of topics, real opportunities for students and postdocs to interact w/ lots of people, chances for older researchers to play soccer and ultimate frisbee, etc.  As travel costs rise and internet connectivity improves, there are going to be sensible reasons to have fewer in-person meetings of otherwise distant participants, but there remains no substitute for a good conversation face-to-face over a coffee or a beer.
• College dorm rooms, while better than when I was a student, are still not high on ambiance.  Generic fitted and top sheets for bedding appear to be made from dryer lint.
• Food options have become progressively healthier and tastier in general.
• Mount Holyoke is a lovely campus, with very loud and happy frogs.
• A session about cuprate superconductors correlated with the literal gathering of storm clouds in an otherwise sunny week.
• About 30% of the audience got the reference (after about a 5 second delay) when, on a slide about magnetic interactions (\(J_{zz} S^{z}_{i} \cdot S^{z}_{j}\)), there was an unlabeled picture of Jay-Z.  

A couple of science thoughts (carefully brief to avoid violating the GRC policy about discussing conference talks and posters):

• Cuprate superconductors remain amazingly complicated, even after years of improving sample quality and experimental techniques. 
• Looking at driven systems is becoming very exciting.  Basically under some circumstances you can use light to flip on or off topological changes in band structure, for example.
• It remains very challenging to figure out how to think about systems with low energy excitations that don't look like long-lived quasiparticles. 

Gordon Conference

I am going to be at the Gordon Research Conference on correlated electrons for the next few days. Should be fun, but blogging about such meetings is generally frowned upon (don't want to discourage people from frank discussions and showing brand new, untried stuff).  There are rules about confidentiality for these meetings.  I'll write more later in the week on other topics.

FeSe on SrTiO3: report of 100 K superconductivity

I'd heard rumors about this for a while.  I presume that the posting of this on the arxiv means that some form of this paper is in submission out there to a suitably glossy, high impact journal that requires reference citations in its abstracts.  Background:  Bulk FeSe superconducts below around 8 K at ambient pressure (see here).  Under pressure, that transition can be squeezed up beyond 35 K (see here).  The mechanism for superconductivity in this material is up for debate, as far as I know (please feel free to add a reference or two in the comments). 

These investigators have a very fancy ultrahigh vacuum system, in which they are able to grow single layer FeSe on top of SrTiO₃ (with the substrate doped with niobium in this case).  This material is not stable in air, and apparently doesn't do terribly well even when coated with some protective layer.  However, these folks have a multi-probe scanning tunneling microscope system in their chamber, along with a cold stage, so that they can perform electrical measurements in situ without ever exposing their single layer to air.  They find that the electrical resistance measured in their four-point-probe configuration drops to zero below around 100 K (as high as 109 K, depending on the sample).  One subtle point that clearly worried them:  SrTiO₃ is know to have a structural phase transition (the onset of ferroelasticity - see here) at around 105 K, so they wanted to be sure that what they saw wasn't somehow an artifact of that substrate effect.  (Makes me wonder what happens to superconductivity in the FeSe depending on the ferroelastic domain orientation underneath it.)  For the lay audience:  liquid nitrogen boils at ambient pressure at 77 K.  This would be the first iron-based superconductor to cross that threshold, a domain previously limited to the copper oxides.   Remember, if the bulk transition is at 8 K and the single layer case exceeds 100 K, it doesn't seem crazy to hope for some related system with an additional factor of three or four that takes us beyond room temperature.

Important caveats:  Right now, they have resistance measurements and tunneling spectroscopy measurements.  Because of the need for in situ measurement they don't have Meissner data.  It's also important to realize that the restrictions here (not air stable; only happens in single layer material when ultraclean) are not small.  At the same time, this is potentially very exciting, and hopefully it holds up well and can be the foundation for more exciting materials.

750th post - blog demographics

This is the 750th post since this blog's inception.  Fun facts gleaned from google analytics:

1) Unsurprisingly, the US leads in blog hits over that time, with 270,648.  In second place, the UK with 26,698.

2) According to google's tracking, over the last nine years there have been hits from every country in North, Central, and South America, as well as Europe.  In Asia, the only countries with zero hits are Turkmenistan and New Guinea.  In Africa, I'm missing about a dozen, basically the sub-Saharan region plus Somalia. 

3) In the US, the state with the least hits is South Dakota (84 visits over nine years), narrowly edging out Wyoming (88) and Alaska (91).   The states with the most hits are Texas, California, New York, and Massachusetts.

4) Most common browser, by a wide margin, is Firefox, followed by Chrome.  I like the idea that someone has read the blog on a PlayStation 3, and someone else on a PlayStation Portable.  Disappointed (and showing my age by that fact) that no one used lynx or emacs.  

5) Most-viewed post of all time was the meme contest.  Most-viewed physics posts were these on plasmons and polarons. 

Thank you all for reading!

"Seeing" chemical bonds with sub-molecular resolution

Chemists (and physicists) often draw molecular bonds as little lines connecting atoms, but actually imaging the bonds themselves is very hard.  With the advent of the scanning tunneling microscope, it's become almost commonplace to be able to image the position of atoms.  STM images the ability of electrons to enter or leave a conducting surface, and since an atom on the surface carry electrons within itself, the presence of an atom on the surface strongly modulates the STM signal.  This doesn't show anything direct about bonding between atoms, however.

Wilson Ho's group at UC Irvine has published another gem.  The paper is here (unfortunately behind the Science paywall), and the news release is here.  The new STM-based imaging technique, "itProbe", is based in inelastic tunneling, which I've described before.  (One advantage in being an ancient blogger - I can now refer back to my old stuff, with google helping me remember what I wrote.)  The Ho group deliberately attaches a CO molecule to their STM tip.  The CO molecule has a couple of very sharp vibrational (and "hindered translational") modes at low energies that can be seen electrically through inelastic electron tunneling spectroscopy (IETS) - basically sharp features in (the second derivative of) the tunneling current-voltage curve.  In the itProbe technique, the experimenters map out spatially what happens to those modes.  The idea is, as the CO molecule interacts with the sample close by, the precise energies of those vibrational modes shift - the environment of the CO molecule tweaks the effective spring constant for the CO's motion.  Imaging in this way, they find that maps of the inelastic signal seem to show the bonds between the atoms in an underlying molecule, rather than the atom positions themselves.  I admit I don't understand the precise mechanism here, but the images are eye-popping.  A similar idea, involving atomic force microscopy with CO attached to an AFM tip, was demonstrated before (here and here, for example).  In those experiments, the investigators looked at how interactions between the CO on the tip and the sample affected the mechanical properties of the tip as a whole.   

This is an example of a tour de force experiment that can be accomplished by long, sustained effort - the Ho group has been refining their IETS measurements for nearly two decades, and it's really paid off.  Hopefully these kinds of efforts will not become even less common as research funding seems to be focused increasingly on short time horizons and rapid changes in fashion.

Bad physics as a marker for tracking text recycling

A colleague of mine was depressed to find, in a reasonably high impact journal, a statement that magnetic nanoparticles obey Coulomb's law, and thus can be manipulated by external magnetic fields.  As far as physics goes, this is just wrong.  Coulomb's law is the mathematical relationship that says that the force between two charges is proportional to the product of their charges and inversely proportional to the distance between them.  This has nothing to do with magnetic nanoparticles. 

I was curious - where did this weird, incorrect statement come from?  I turned to google to find out.  The earliest result I can find is from this paper by Pankhurst, Connolly, Jones, and Dobson.  The paper seems quite good, and the (strange to me) Coulomb's Law language appears to be some shorthand for a physically sound description of the interactions of magnetic materials with magnetic fields.  The Pankhurst paper includes the following sentence:  "Second, the nanoparticles are magnetic, which means that they obey Coulomb’s law, and can be manipulated by an external magnetic field gradient." This is part of a paragraph that lists three virtues of magnetic nanoparticles for biological applications.  


For fun, try copy/pasting that sentence into google.  Look at how many times that sentence (indeed, that whole introductory paragraph with very minimal changes) shows up nearly verbatim in other publications.  At the risk of saying something actionable, this is plagiarism.   This tends to happen in obscure proceedings, edited book chapters, etc., rather than high impact literature.  The proliferation of shady publication houses and vanity press journals only aggravates this situation.  Very depressing.

My views on teaching "nano"

Blatant self-promotion time:  I was grateful for the invitation to write an editorial about teaching "nano" for Nature Nanotechnology.  The full text is available for free at the above link, and comments and feedback are invited below.  (As a blog reader, you get the added bonus of reading the analogy I made that was cut due to space constraints.  When I advise becoming an expert in a traditional discipline first before tackling an interdisciplinary field, I had written:  "To make a food analogy, it would be very difficult to become an expert at Korean/Mexican fusion cuisine if you did not first know Korean and/or Mexican cooking at a high level.") 

What is chemical potential?

I've been meaning to do a post on this for a long time.  Five years ago (!) I wrote a post about the meaning of temperature, where I tried to go from the intuitive understanding given by common experience (temperature has something to do with energy content, and that energy flows from hot things to cold things) to a deeper view (that flow of energy comes from the tendency of the universe to take on macroscopic configurations that correspond to the most common ways of arranging microscopic degrees of freedom - the 2nd law of thermodynamics, basically).  I wasn't very satisfied with how the post turned out, but c'est la vie.

Chemical potential is a similar idea, but with added complications - while touch gives us an intuition for relative temperatures, we have no corresponding sense for chemical potential; and the rigorous definition of chemical potential is more complicated.  (For another take on this, see this article, available in full text via google from a variety of sources.)

Let's reason by analogy with temperature.  Energy tends to flow from a system at high temperature to a system at low temperature; when systems with identical temperatures are brought into contact so that they may exchange energy (e.g., by thermal conduction), there is no net flow of energy.  Now suppose systems are able to exchange particles as well as energy.  If two systems are at the same temperature, then particles will tend to flow from the system of higher chemical potential (one of the several parameters denoted by the symbol \(\mu\)) to that of lower chemical potential.  If two systems have identical chemical potentials for a particular kind of particle, there will be no net flow of particles.  In general, particles tend to flow from regions of high \(\mu/T\) to regions of low \(\mu/T\).  The classic example of this is the case of a closed bottle of perfume in a room full of (non-perfumed) air.  The perfume molecules have a high \(\mu\) in the bottle relative to the rest of the room.  When the bottle is opened, perfume molecules will tend to diffuse out of the bottle, simultaneously lowering their \(\mu)\) in the bottle and increasing their \(\mu\) in the room.  This will continue until the chemical potentials equalize.  From the point of view of entropy, there are clearly very many more arrangements of molecules with them roughly spread throughout the room+bottle than the number of arrangements with the molecules happening to occupy just the bottle.  Hence, the universe tends toward the macroscopic configuration corresponding to the most microscopic configurations.  Bottom line:  equilibrium between two systems that can exchange particles requires equal temperatures and equal chemical potentials. 

Where this also gets tricky is that thermodynamics tells us that \(\mu\) also corresponds to the energy per particle required to add (or remove) one particle from the system at constant temperature and pressure (!).  This identity is not at all obvious from the above description, but it's nevertheless true.  This latter way of thinking about chemical potential means that when particles can couple to some "real" potential (gravitational, electrical), it is possible to tune their total \(\mu\).  The connection to the entropic picture is the idea that particles will tend to "fall downhill" (there are usually fewer configurations of the combined system that have some particles "stacked up" in a region of high potential energy with others in a region of low potential energy, than the situation when the energy gets spread around among all the particles). 

Prize season again - updated w/ Kavli winners

Once again the Breakthrough Prize and New Horizons Prize in fundamental physics are seeking nominations.  See here.  I have very mixed feelings about these prizes, given how the high energy theory components seem increasingly disconnected from experiment (and consider that a feature rather than a bug).

On a related note, the Kavli Prizes are being awarded this Thursday.  Past nanowinners are Millie Dresselhaus (2012), Don Eigler (love his current affiliation) and Nadrian Seeman (2010), and Louis Brus and Sumio Iijima (2008).   Not exactly a bunch of underachievers.  Place your bets.  Whitesides?  Alivisatos and Bawendi?

Update:  Thomas Ebbeson (extraordinary transmission through deep sub-wavelength apertures, thanks to plasmons), Stefan Hell (stimulated emission depletion microscopy, for deep subwavelength fluorescence microscopy resolution), and John Pendry (perfect lenses and cloaking).  Congratulations all around - all richly deserved.  I do think that the Kavli folks are in a sweet spot for nano prizes, as there is a good-sized pool of outstanding people that has built up, few of whom have been honored already by the Nobel.  This is a bit like the early days of the Nobel prize, though hopefully with much less political infighting (see this book if you really want to be disillusioned about the Nobel process in the early years).

Workshop on structural and electronic instabilities in oxide nanostructures

I've spent the last two days at a fun "Physics at the Falls" workshop at the University of Buffalo.  It's been cool learning about the impressive variety of physics at work in these systems.  A few takeaways:

• With enough stainless steel and high tech equipment you can grow (and in situ characterize with everything from electron diffraction to photoemission, angle-resolved and otherwise) just about anything these days!
• There's a lot of pretty work getting done growing epitaxial complex oxides down to the single unit cell level, and a lot of accompanying extremely high resolution transmission electron microscopy.
• Untangling thermal effects from optical effects in nonequilibrium experiments can be tricky.  Interesting to see that lower energy photons can be more efficient at kicking systems from one phase to another than photons much more energetic than any energy gap.
• There does seem to be some convergence on understanding LAO/STO oxide heterojunctions.
• We still don't understand superconductivity in strontium titanate, even though it's been known for decades.
• Orbitals really matter, when you are dealing with relatively localized electrons.
• Niagara Falls is very impressive!

Slow blogging + interesting links

The end of our academic year + travel + some major writing has cramped my blogging of late.  Things should pick back up to a more regular pace in a couple of weeks.  In the meantime, here are some links that caught my eye lately:

• On Sir Harold Kroto's website, here are some interesting lectures by Richard Feynman.  It's absolutely worth browsing around the rest of the site, too - lots of cool videos.
• This preprint by Sean Hartnoll looks very interesting.  There are materials out there that act like metals (in the sense of having lots of low energy excitations available, and an electrical resistivity that falls with decreasing temperature), but the electrons interact so strongly and in such a complex way that it no longer makes sense to think about "quasiparticles" that act basically like ordinary electrons.  The challenge is, if the quasiparticle picture (which works spectacularly well for materials like gold, copper, aluminum, doped semiconductors) fails, what's the right way to treat these systems?  This paper tries to look at what features would have to be there in such a system.
• This video is cute.  The material used in this LED has a bandgap that apparently increases a fair bit upon cooling.  As a result, the light emitted from the diode shifts toward the blue when the device is dipped in liquid nitrogen, and comes back toward the red when it's warmed.
• We still really don't understand triboelectricity, the "static electricity" you see when you rub a balloon against your hair or rub a glass rod with rabbit fur.  News story here.  It's amazing to me that we still don't know how this kind of charge transfer works, given that it was discovered thousands of years ago.  (As Pauli said, "God made the bulk; surfaces were the work of the devil.")

What are the Kramers-Kronig relations, physically?

Let me pose a puzzle.  Suppose you are in a completely dark room.  You know that at some point in the future, someone will turn on a light in that room for a few minutes, and then turn it off later.  Being a mathematically sophisticated person, it occurs to you that you could think about the time dependence of the electric field in the room.  It's zero for a while, oscillating (b/c that's what happens when there is light there) for a few minutes, and then zero again.  Being clever, you think about Fourier transforming that time dependence, and thinking about all the frequencies in there - the fact that the room right now is dark is actually because of the amazing cancellation of a whole bunch of frequency components!  Therefore, you should be able to put on glasses that are frequency-filtering, block out some of those components, and suddenly be able to see in a dark room!  Except that totally doesn't work, even in a completely classical world without photons.  Why not? 

Think about a material placed in a time-varying (say, harmonically varying, because that's what physicists like) electric field.  The material responds in some way - electrons rearrange themselves within the material in response to that electric field; if the field is slow enough, atoms or groups of atoms can even shift their positions.  The result is a polarization density (electric dipole moment per unit volume) \(\mathbf{P} \equiv \chi_{e}\mathbf{E}\).  Here \( \chi_{e}\) is the electric susceptibility (generally a tensor, meaning that \(\mathbf{P}\) and \(\mathbf{E}\) don't have to point in the same direction).  The dielectric function of a material is defined \(\epsilon \equiv \epsilon_{0}(1 + \chi_{e})\).  In general, the response of the material depends on the frequency \(\omega\) of the electric field, and it can be out of phase with the external electric field.  This is described in mathematical shorthand by considering \(\epsilon(\omega)\) to be complex, having real and imaginary components.

The Kramers-Kronig relations are fairly intimidating looking integral expressions that describe relationships that have to be obeyed between the real and imaginary components of \(\epsilon(\omega)\).  These relationships come from the fact that \(\mathbf{P}\) now can only depend on \(\mathbf{E}\) in the past, up until now.  This restriction of causality, plus the properties of Fourier transforms, are what leads to the K-K integrals.  The wikipedia page about this actually has a very nice description here.   So, while the math is not something that most people would think of as obvious, the basic idea (electromagnetic fields influence materials in a causal way, and that places constraints on how materials can respond as a function of frequency) is not too surprising.

National Nano Infrastructure Network - feedback requested

I wrote before about the saga of the NNIN and how painful the outcome was this year - no awards made, after thousands of person-hours invested on the writing and reviewing of proposals.  Well, NSF is requesting input, in part because they want guidance on structuring the new solicitation to come out this autumn.  So, please give your input if you're in the US and think this kind of support for shared infrastructure is valuable.  By the way, if it seems like NSF had already gone through an exercise like this before the last solicitation (the one where they didn't fund anyone), you're right - they even had a two-day workshop and produced a report.

Recurring themes in (condensed matter/nano) physics: Fermi's Golden Rule

Very often in condensed matter (or atomic) physics we are interested in trying to calculate the rate of some quantum process - this could be the absorption of photons by an isolated atom or a solid, for example.  In (advanced) undergraduate quantum mechanics, we can apply time-dependent perturbation theory to do such a calculation.  Typically you assume that the system starts in some initial state \( |i\rangle \), is subjected to some perturbation \(V\) that turns on at time \(t = 0\), and ends up in final state \( |f\rangle \).  If \(V\) has a harmonic time dependence with some (angular) frequency \(\omega\), then you can do a nice bit of math that calculates the rate at which this process happens.  You discover that at long times the only allowed transitions are the ones where the energies of the initial and final states differ by \(\hbar \omega\), and that the rate of that process is \( (2\pi/\hbar) |\langle i |V| f\rangle|^{2} \rho \), where \(\rho\) is the number of states per unit energy per unit volume that satisfy the energy constraint.

This result, associated with Enrico Fermi, shows up over and over, with some common motifs in condensed matter and nanoscale physics, at least in spirit (that is, sometimes people apply heuristically even though the perturbation may not be harmonic, for example).  First, the \( |\langle i |V| f\rangle|^{2} \) term is what gives us selection rules.  If you think about optical transitions in atoms, this is why you get electric dipole transitions from the 2\(p\) state of hydrogen to the 1\(s\) state, rather than from the 2\(s\) state; in the latter, this quantity is zero.  In crystalline solids, if the initial and final states are Bloch waves, it's the periodicity of the lattice that makes this quantity zero unless (crystal) momentum is conserved.  This is the root of the idea that processes ordinarily forbidden in macroscopic crystals can sometimes take place in nanocrystals or at surfaces.

Similarly, meso- and nanoscale systems can greatly constrain \( \rho \).  One reason that you can get very long mean free paths for charge carriers in semiconductor nanowires, carbon nanotubes, graphene, at the edges of quantum Hall systems, etc., is that the density of states available into which carriers can scatter is very restricted.  Similarly, enhancing \(\rho\) can pay dividends - this is the source of the Purcell effect, where radiative transition rates can be greatly enhanced by increasing the photon density of states, and is part of the reason for enhanced rates of optical processes near plasmonic nanostructures.

updated - Physics education and real world perspective

I was absolutely horrified to read about this story, about how more than 200 girls were kidnapped in Nigeria by a radical Islamic group because they had the temerity to show up for a physics test (emblematic of getting a Western education).  I fervently hope that there is enough public outrage about this to get some positive action there, though it's hard to be optimistic.

Stories like this should remind many of us how petty our concerns (departmental rankings; referee comments; grant reviews; tenure decisions; grad school admissions decisions) really are, even if they seem stressful and important.  It is terrible that in the 21st century there are still large segments of the world where modern learning is expressly forbidden, on pain of death.

Update:  Uggh.  It would appear that the abducted girls have been forcibly married off.  There are so many things wrong here that it's hard to know where to begin.

Informal survey: How important are departmental rankings?

Coincident with the annual US graduate school admission season, I've had a few conversations in recent days where the topic of departmental rankings has come up.  I've written about this general topic before (here and here, for example).  I want to perform a non-serious (in the sense that it's a self-selected survey population that may well be atypical) survey here of those applying to grad school, currently in grad school, or recently (say within the last 4 years) completing grad school:  How important were official rankings (e.g., US News; NRC) of graduate programs in your grad school application process (where you decided to apply) and in your eventual decision?  

Recurring themes in (condensed matter/nano) physics: spatial periodicity

A defining characteristic of crystalline solids is that their constituent atoms are arranged in a spatially periodic way.  In fancy lingo, the atomic configuration breaks continuous translational and rotational invariance (that is, it picks out certain positions and orientations in space from an infinite variety of possible choices), but preserves discrete translational invariance (and other possible symmetries).  

The introduction of a characteristic spatial length scale, or equivalently a spatial frequency, is a big deal, because when other spatial length scales in the physical system coincide with that one, there can be big consequences.  For example, when the wavelength of x-rays or electrons or neutrons is some integer harmonic of the (projected) lattice spacing, then waves scattered from subsequent (or every second or every third, etc.) plane of atoms will interfere constructively - this is called the Bragg condition, is what gives diffraction patterns that have proven so useful in characterizing material structures.  Another way to think about this:  The spatial periodicity of the lattice is what forces the momentum of scattered x-rays (or electrons or neutrons) to change only by specified amounts.

It gets better.  When the wavelength of electrons bound in a crystalline solid corresponds to some integer multiple of the lattice spacing, this implies that the electrons strongly "feel" any interaction with the lattice atoms - in the nearly-free-electron picture, this matching of spatial frequencies is what opens up band gaps at particular wavevectors (and hence energies).  Similar physics happens with lattice vibrations.  Similar physics happens when we consider electromagnetic waves in spatially periodic dielectrics.  Similar physics happens when looking at electrons in a "superlattice" made by layering different semiconductors or a periodic modulation of surface relief.

One other important point.  The idea of a true spatial periodicity really only applies to infinitely large periodic systems.  If discrete translational invariance is broken (by a defect, or an interface), then some of the rules "enforced" by the periodicity can be evaded.  For example, momentum changes forbidden for elastic scattering in a perfect infinite crystal can take place at some rate at interfaces or in defective crystals.  Similarly, the optical selection rules that must be rigidly applied in perfect crystals can be bent a bit in nanocrystals, where lattice periodicity is not infinite.

Commensurate spatial periodicities between wave-like entities and lattices are responsible for electronic and optical bandgaps, phonon dispersion relations, x-ray/electron/neutron crystallography, (crystal) momentum conservation and its violation in defective and nanoscale structures, and optical selection rules and their violations in crystalline solids.  Rather far reaching consequences!

End of an era.

As long as we're talking about the (alleged) end of science, look at this picture (courtesy of Don Monroe).  This is demolition work being done in Murray Hill, NJ, as Alcatel-Lucent takes down a big hunk of Building 1 of Bell Labs. 

This building and others at the site were the setting for some of the most important industrial research of the 20th century.  (Before people ask, the particular lab where the transistor was first made is not being torn down here.)  I've written before about the near-demise of long-term basic research in the industrial setting in the US.  While Bell Labs still exists, this, like the demise of the Holmdel site, are painful marks of the end of an era.

John Horgan: Same old, same old.

John Horgan writes about science for National Geographic.  You may remember him from his book, The End of Science.   His thesis, 17 years ago, was that science is basically done - there just aren't going to be too many more profound discoveries, particularly in physics, because we've figured it all out and the rest is just details.  Well, I'll give him this for consistency:  He's still flogging this dead horse 17 years later, as seen in his recent column.  I disagree with his point of view.  Even if you limit yourself to physics, there are plenty of discoveries left to be made for a long time to come - things only look bleak if (a) you're only a reductionist; and (b) you limit your interest in physics to a narrow range of topics.  In other words, possibly looking for supersymmetric partners at the LHC might not be a great bet, but that doesn't mean that all of science is over.

A video interview for an online nano course

Two of my colleagues (Dan Mittleman and Vicki Colvin) put together a Coursera class this past year, "Nanotechnology:  The Basics", and as part of that they interviewed several Rice faculty about different bits and pieces.   They spoke to me about nanoelectronics, but the conversation ended up ranging into a discussion of hype in science and the importance of communicating to a general audience.  The video is now up online here, and the hype/science presentation discussion starts at around 18:38. 

Recurring themes in (condensed matter/nano) physics: hybridization

Suppose I have two identical systems, such as two copies of a mass attached to a spring (anchored to an immovable wall).  Each system by itself has some characteristic response, like a frequency of motion, and those responses are identical because the independent systems are identical.  Now consider coupling the two systems together, such as linking the two masses by another (weak) spring, and ask what the total coupled system response looks like.  With classical oscillators like our example, we would say that we find the "new normal modes" of the coupled system - instead of writing separate equations to describe Newton's laws for each mass separately, we can do some kind of change of variables and consider new coordinates that combine the motions of the two masses.  When we do this, we end up again with two characteristic frequencies (basically two effectively independent oscillators), but now the frequencies differ a bit, one being higher and one being lower than the original independent oscillator frequency.  You can generalize this to \(N\) oscillators and find \(N\) new normal modes with a band of frequencies, with the bandwidth determined by the strength of the couplings.

This coupling+splitting the modes crops up again and again.  You can use this to make an electronic band pass filter by capacitively coupling together a bunch of \(LC\) circuits.  You can make a mechanical band pass filter by elastically coupling together a bunch of mechanical oscillators.  You can make a miniband of electronic states by coupling together a bunch of quantum wells that each individually would have identical bound states.  You can make a band of electronic states by coupling together the single-particle atomic states of a periodic array of atoms.  The stronger the coupling, the wider the resulting bandwidth.  This basic idea (taking noninteracting systems, coupling them, and re-solving for new effectively noninteracting modes) is so powerful that when it doesn't work sometimes, it can be jarring.  

Any advice: LaTeX and makeindex

Readers - For a long time now I have been working on a very large LaTeX document (actually built out of a number of sub-documents) that I will discuss further in later posts.  I greatly desire to create an index for this document, and I know about the LaTeX package \makeindex.   The question is, does anyone know of a good frontend application that can make the creation of the index less tedious?  The brute force approach would require me to go through the document(s) by hand and insert a \makeindex tag every time a term that I wish to index appears.  For an index containing a couple of hundred entries, this looks excruciating.  What I would love is an application where I identify the terms for which I want index entries, and it then automatically inserts the appropriate tags (in a smart way, not putting tags inside LaTeX equations, for example).  While this would be imperfect, it would be easier to start from an over-complete index and pare down or modify than to start from scratch.  Yes, I am sure I could use perl or another scripting language to make something, but I'd rather not reinvent the wheel if someone has already solved this problem.  Thanks for any suggestions.

Recurring themes in (condensed matter/nano) physics: boundary conditions

This is the first in a series of posts about tropes that recur in (condensed matter/nano) physics.  I put that qualifier in parentheses because these topics obviously come up in many other places as well, but I run across them from my perspective.

Very often in physics we are effectively solving boundary value problems.  That is, we have some physical system that obeys some kind of differential equations describing the spatial dependence of some variable of interest.  This could be the electron wavefunction \( \psi(\mathbf{r})\), which has to obey the Schroedinger equation in some region of space with a potential energy \( V(\mathbf{r})\).  This could be the electric field \( \mathbf{E}(\mathbf{r})\), which has to satisfy Maxwell's equations in some region of space that has a dielectric function \( \epsilon(\mathbf{r})\).  This could be the deflection of a drumhead \( u(x,y) \), where the drumhead itself must follow the rules of continuum elasticity.  This could be the pressure field \( p(z) \) of the air in a pipe that's part of a pipe organ. 

The thread that unites these diverse systems is that, in the absence of boundaries, these problems allow a continuum of solutions, but the imposition of boundaries drastically limits the solutions to a discrete set.  For example, the pressure in that pipe could (within reasonable limits set by the description of the air as a nice gas) have any spatial periodicity, described by some wavenumber \(k\), and along with that it would have some periodic time dependence with a frequency \(\omega\), so that \( \omega/k = c_{\mathrm{s}}\), where \(c_{\mathrm{s}}\) is the sound speed.  However, once we specify boundary conditions - say one end of the pipe closed, one end open - the rules that have to be satisfied at the boundary force there to be a discrete spectrum of allowed wavelengths, and hence frequencies.   Even trying to have no boundary, by installing periodic boundary conditions, does this. This general property, the emergence of discrete modes from the continuum, is what gives us the spectra of atoms and the sounds of guitars.

How should philanthropists and foundations fund science?

This article from the NY Times discusses the funding of science research by wealthy individuals and, by extension, philanthropic foundations set up by those folks.  It brings up an issue that I phrased in the form of a question as the title of this post.  I'm not going to offer any simple overarching answer, but I do want to make a couple of observations (strictly my opinion, of course):

• Many wealthy people and foundations support medical research.  This makes a lot of sense - generally philanthropists want to Help People, and supporting research that directly affects medical care and quality of life is a completely sensible choice.
• A smaller number of people and foundations support research in the physical sciences and engineering; like those who support medical research, they want to Help People, and they realize that supporting basic research and the education of technically skilled and creative people is a great way to do that.
• Both groups, however, face the challenge that any investment that they make is basically a drop in the bucket compared with what governments can do.  NIH puts tens of billions of dollars a year into medical research.  NSF's annual budget is around $7B.  
• In my experience, the philanthropic supporters of science are well aware of this - if they want to make sure that their money makes a difference, they need to invest in supporting things that are not what government agencies are already doing.  Their challenge, then, is to identify areas (and eventually institutions and people) where their investment will really move the needle.  Of course, they need to be able to tell wheat from chaff.  Peer review is a customary way to do this, and that is often how the government agencies (most of them, anyway) make judgments, but peer review tends toward being risk averse.  An alternative is to have a dedicated science board to do reviews and make decisions.  This, too, is tricky, particularly if the members aren't exact subject matter experts.  How much weight should be placed on prior track record?  Researchers who are senior and already have major awards, etc. can be a lower risk - they have already demonstrated that they can do great work.  On the other hand, if someone is already extremely well supported (as such people often are), how much difference will philanthropic support really make?  It seems like a very tricky decision process, particularly depending on the amounts involved.  
• There is no question that having grants with wide flexibility (e.g., Packard; presumably MacArthur) can be wonderful.  At the single investigator level, there is also no question that there can be real benefits from being able to concentrate on actual science - that's an argument for funding support large enough that it allows investigators to lay off writing other grants to some extent.  (That's one aim of things like the Howard Hughes Investigator program.)  

Feel free to comment below.  Perhaps additional philanthropic support is one way to get more "scientific mavericks" (as long as that doesn't mean funding of unfounded crazy stuff).  

Taking a few days, + a philanthropy suggest for Google or Intel

Last post for a few days.  I want to make a suggestion, though.  Hey large tech companies, like Intel or Google, or for that matter Sematech or the SRC, or foundations like Keck, Moore, Packard, MacArthur:  You may have heard that NSF seems to have put shared physical sciences research infrastructure on the back burner.   I firmly believe that this is a bad decision that will have lasting negative consequences for many people.  I've written before about how much impact on science and engineering research and education there would be if companies (or individuals, I suppose, if they were sufficiently wealthy) would step forward and endow shared research equipment and staffing at universities.   Now is the time, when there is likely to be a real federal gap here.  I'm serious, and I'd be happy to talk with any interested parties about how this could be done - just email me. 
Update:  this is highly relevant.

Coolest paper of 2014 so far, by a wide margin.

Sorry for the brief post, but I could not pass this up.

Check this out:  http://arxiv.org/abs/1403.1211

I bow down before the awesomeness of an origami-based microscope. 

March Meeting wrap-up

I've been slow about writing a day 3/4/wrapup of the APS meeting because of general busy-ness.  I saw fewer general interest talks over that last day and a half in part because my own group's talks were clustered in that timeframe.  Still, I did see a couple of interesting bits.

• There was a great talk by Zhenchao Dong about this paper, where they are able to use the plasmonic properties of a scanning tunneling microscope tip to perform surface-enhanced Raman spectroscopy on single molecules (in ultrahigh vacuum and cryogenic conditions) with sub-nm lateral resolution.  The data are gorgeous, though how the lateral resolution can possibly be that good is very mysterious.  Usually the lateral extent of the enhanced optical fields is something like the geometric mean of the tip radius of curvature and the tip-sample distance.  It's very hard to see how that ever gets to the sub-nm level, so something funky must be going on.
• I saw a talk by Yoshihiro Iwasa all about MoS₂, including work on optics and ionic liquid gating.  
• I went to a session on the presentation of physics to the public.  The talks that I managed to see were quite good, and Dennis Overbye's insights into the NY Times' science reporting were particularly interesting.  He pointed out that it's a very challenging marketplace when so much good (or at least interesting) science writing is given away for free (as in here or here or here).  He did give a shout-out to Peter Woit, particularly mentioning how good Peter's sources are.

I probably should wade into focus topic organizing again;  it seemed like this year there were more issues with parallel sessions about similar topics and some lack of cohesiveness within some of the contributed sessions.  (This isn't meant as a criticism of those who invested their time to do this, which is absolutely appreciated!  I am well aware how hard it is, particularly as the meeting keeps growing.)

The end of the National Nano Infrastructure Network? Federal support for shared facilities.

The National Nanotechnology Infrastructure Network is, as their page says, "an integrated networked partnership of user facilities, supported by the National Science Foundation, serving the needs of nanoscale science, engineering and technology".  Basically, the NNIN has been a mechanism for establishing nodes of excellence at sites around the US, where people could travel to use equipment and capabilities (high resolution transmission electron microscopy; sophisticated wafer-scale electron beam lithography; deep etching) that they lack at their home institutions.  Crucially, these shared facilities are supported by skilled technical staff that can train users, work with users to develop processes, perform fee-for-service work on occasion, etc.  The most famous sites are the Stanford Nanofab Facility and the Cornell Nanofab.  Over the years, the NNIN has been instrumental in an enormous amount of research progress.  Note that this effort is distinct from Major User Facilities (such as synchrotrons, neutron sources, etc).

This year, there was a competition for a Next Generation NNIN - the call is here.  The idea was very much to broaden the network into characterization as well as fabrication, and to reach new, growing communities of users in areas like bio, the environment, earth sciences/geo.  After a proposal process that boiled down to two teams (one with 18 universities; one with 20), very extensive full proposals, reverse site visits, written responses to reverse site visits and reviews, etc., the NSF decided not to make an award.  It would appear that there will be another call of some kind issued in fall, 2014.  For now, what this means is that the NNIN is ending.  Cornell, Stanford, and the other sites face major cuts in funding for staff and support for external users.  (Full disclosure:  I was the Rice rep on one of the teams.)

This whole issue is very complex, but it raises a number of questions that would benefit from a discussion in the community.  What should be the pathway to federal support for shared facilities and staffing, particularly tools and techniques that would be prohibitively expensive for individual universities to support via internal funds?  Should there be federal support for this?  Should it come from NSF?  How can we have a stable, sustained level of research infrastructure, including staffing, that serves the broad scientific community, in an era when funding is squeezed ever more tightly?  If the burden is shifting more toward individual universities having to support shared infrastructure basically with internal funding and user fees, what impact will that have?  Comment is invited.

UPDATE:  Here is a story that Science is running regarding the decision, or lack thereof. 

March Meeting, Day 2

This is a meta-post - I'm writing it while sitting in the back of a session on presenting science to the public.  A brief list of some of the neat things I heard yesterday:

• I saw a very nice talk by Jelena Vuckovic about doing nonlinear and cavity optics, with (self-assembled InAs) quantum dots as the emitters, and the cavity being formed in 2d photonic band gap systems.  The latest work looks at nonlinear effects like photon blockade, and makes contact to some work involving "circuit" quantum electrodynamics (see here).
• I went to a talk by Ken Golden, who taught me sophomore differential equations, and he gave a fascinating presentation about applying rigorous math (percolation theory, treating microstructured composites like effective media) to the challenging problem of understanding melting polar sea ice.  As a side note, he showed a great picture that is an example of the "quasistatic limit" - long wavelength surface ocean waves don't "see" individual ice floes, but instead propagate in an effective medium.
• There was a great invited session about oxide heterostructures.  Mobilities are improving (under the right conditions) to the point where some ways of learning about the band structure through electronic transport are now becoming possible.  Very impressive was a talk by Shahal Ilani, where he presented a very compelling view of the importance of structural domains ("ferroelasticity") in the underlying strontium titanate - when those domains are under control, transport becomes much more clean, revealing the apparent existence of a magnetically interesting phase at high carrier density and high in-plane magnetic field.

March Meeting, Day 1

Observations from the first day of the APS March Meeting:

• There has been a lot of progress and excitement in looking at layered materials "beyond graphene".  It's interesting to see a resurgence of interest in transition metal (Ti, but more frequently W and Mo) dichalcogenides (S, Se, Te), a topic of great activity in bulk materials growth in the 1970s and early 80s.  There are clearly a lot of bright people working on ways to grow these materials layer-by-layer, with the long-term idea of making structures somewhat like semiconductor heterostructures (e.g., GaAs/AlGaAs), but with the richer palette provided by these materials (exhibiting charge density waves, strong spin-orbit effects, complex band structure, etc.).  Molecular beam epitaxy of these materials with high quality is generally very hard.  For example, Mo and W are extremely refractory, requiring electron beam evaporation at temperatures exceeding 2500 C, and sticking at the sample surface without much diffusion.  Whoever really gets layer-by-layer, large-area growth working with diverse materials is going to make a big impact.
• I saw Heinrich Jaeger give a great talk about granular materials by design.  These are entirely classical systems, but they are extremely challenging.  If you think about it, they are not crystalline (no long-range symmetries to exploit in modeling), they are non-ergodic (the constituent grains are kinetically limited, and can't explore all possible configurations), and nonlinear (the interactions between particles are short-ranged and very strong).  Very interesting.
• I caught two talks in the session looking at silicon-based quantum information processing.  It's possible to create and manipulate dangling bonds on the Si surface (localized states that can trap electrons) and look at how those bonds interact with each other.  Very neat.  Looking at particular individual impurities, with the right system (erbium in Si), you can couple a single impurity to a single-electron transistor charge sensor.  Then, you can manipulate that impurity with optical techniques and use the charge detection to determine its state.  Very impressive.
• The session on secrecy in science was very good.  The ability to manufacture viruses by design is genuinely frightening (though it loses some menace when the words "Pandemic - millions of deaths?" are projected in Comic Sans).  The discussion of intellectual property was great and the role of universities merits its own blog post.  Lastly, I was unaware of the WATCHMAN project, which is a very interesting neutrino physics experiment that as an added bonus should allow the international community to detect rogue nuclear reactors meant for weapons development.