Lab conditions

I disagree with this comic, though I can never get my students or our facilities people to back my idea of converting the entire lab into ultrahigh vacuum space.  Sure, spacesuits would be required for lab work, but think of all the time we would save swapping samples and pumping out our evaporator.

Referees

In the world of scientific peer review, I think that there are three kinds of referees:  those that help, those than hinder, and those that are, umm, ineffective.  Referees that are ineffective do an adequate surface job, looking over papers to make sure that there are no glaring problems and that the manuscript is appropriate for the journal in question, but that's it.  Referees that hinder are the annoying ones we all complain about.  You know - they're the ones that send in a twelve word review for your groundbreaking submission to Science or Nature after sitting on it for 6 weeks; the review says little except "Meh." and may even indicate that they didn't really read the paper.  They're the ones that say work is nice but not really original, with no evidence to back up that statement.  They're the ones who sit on papers because they're working on something similar.  

Referees that help are the best kind, of course.  These are the people who read manuscripts carefully and write reports that end up dramatically improving the paper.  They point out better ways to plot the data, or ask for clarification of a point that really does need clarification or improved presentation.  They offer constructive criticism.  These folks deserve our thanks.  They're an important and poorly recognized component of the scientific process.

Obama gets behind science education

Thanks to Phil Plait for pointing this out.  Awesome!

Graphene, part II

One reason that graphene has comparatively remarkable conduction properties is its band structure, and in particular the idea that single-particle states carry a pseudospin.  This sounds like jargon, and until I'd heard Philip Kim talk about this, I hadn't fully appreciated how this works.  The idea is as follows.  One way to think about the graphene lattice is that it consists of two triangular lattices offset from each other by one carbon-carbon bond length.  If we had just one of those lattices, you could describe the single-particle electronic states as Bloch waves - these look like plane waves multiplied by functions that are spatially periodic with reference to that particular lattice.  Since we have two such lattices, one way to describe each electronic state is as a linear combination of Bloch states from lattice A and lattice B.  (The spatial periodicity associated with lattice A (B) is described by a set of reciprocal lattice vectors that are labeled K (K'))

Here is where things get tricky.  The particular linear combinations that are the real single-particle eigenstates can be written using the same Pauli matrices that are used to describe the spin angular momentum of spin-1/2 particles.  In fact, if you pick a single-particle eigenstate with a crystal momentum \hbar k, the correct combination of Pauli matrices to use would be the same as if you were describing a spin-1/2 particle oriented along the same direction as k.  This property of the electronic states is called pseudospin.  It does not correspond to a real spin in the sense of a real intrinsic angular momentum.  It is, however, a compact way of keeping track of the role of the two sublattices in determining the properties of particular electronic states.  

The consequences of this pseudospin description are very interesting.  For example, this is related to why back-scattering is disfavored in clean graphene.  In pseudospin language, a scattering event that flips the momentum of a particle from +k to -k would have to flip the pseudospin, too, and that's not easy.  In non-pseudospin language, that kind of scattering would have to change the phase relationship between the A and B sublattice Bloch state components of the single-particle state.  From that way of phrasing it, it's more clear (at least to me) why this is not easy - it requires rather deep changes to the whole extended wavefunction that distinguish between the different sublattices, and in a clean sample at T = 0, that shouldn't happen.

A good overview of this stuff can be found here (pdf) in this article from Physics Today, as well as this review article.  Finally, Michael Fuhrer at the University of Maryland has a nice powerpoint slide show (here) that discusses how to think about the pseudospin.  He does a much more thorough and informative job than I do here.

Not even wrong.

No, this is not a reference to Peter Woit's blog.  Rather, it's my reaction to reading this and the other pages at that domain.  Wow.  Some audiophiles must really be gullible.

Graphene, part I

Graphene is one of the hottest materials out there right now in condensed matter physics, and I'm trying to figure out what tactic to take in making some blog postings about it.  One good place to start is the remarkably fast rise in the popularity of graphene.  Why did it catch on so quickly?  As far as I can tell, there are several reasons.

1. Graphene has a comparatively simple electronic structure.  It's a single sheet of hexagonally arranged carbon atoms.  The well-defined geometry makes it extremely amenable to simple calculational techniques, and the basic single-particle band structure (where we ignore the fact that electrons repel each other) was calculated decades ago.
2. That electronic structure is actually pretty interesting, for three reasons.  Remember that a spatially periodic arrangement of atoms "picks out" special values of the electron (crystal) momentum.  In some sense, electrons with just the right (effective) wavelength (corresponding to particular momenta) diffract off the lattice.  You can think of the hexagonal graphene lattice as a superposition of two identical sublattices off-set by one carbon-carbon bond length.  So, the first interesting feature is that there are two sets of momenta ("sets of points in reciprocal space") that are special - picked out by the lattice, inequivalent (since the two sublattices really are distinct) but otherwise identical (since it's semantics to say which sublattice is primary and which is secondary).  This is called "valley degeneracy", and while it crops up in other materials, the lattice symmetry of graphene ends up giving it added significance.  Second, when you count electrons and try filling up the allowed electronic states starting at the lowest energy, you find that there are exactly two highest energy filled spatial states, one at each of the two lowest-momentum inequivalent momentum points.  All lower energy states are filled; all higher energy states are empty.  That means that graphene is exactly at the border between being a metal (many many states forming the "Fermi surface" between filled and empty states) and a semiconductor (filled states and empty states separated by a "gap" of energies for which there are no allowed electronic states).  Third and most importantly, the energy of the allowed states near those Fermi points varies linearly with (crystal) momentum, much like the case of an ultrarelativistic classical particle, rather than quadratically as usual.  So, graphene is in some ways a playground for thinking about two-dimensional relativistic Fermi gases.
   
3. The material is comparatively easy to get and make.  That means its accessible, while other high quality two-dimensional electron systems (e.g., at a GaAs/AlGaAs interface) require sophisticated crystal growth techniques.
4. There is a whole literature of 2d electron physics in Si and GaAs/AlGaAs, which means there is a laundry list of techniques and experiments just waiting to be applied, in a system that theorists can actually calculate.
5. Moreover, graphene band structure and materials issues are close to that of nanotubes, meaning that there's another whole community of people ready to apply what they've learned.
6. Graphene may actually be useful for technologies!

Next time I post about this, I'll try to talk more about the special aspect of the valley degeneracy.

Feedback time.

So, readers - any requests for particular topics, or hot tips on things I've missed?

Philip Kim visits Rice; I visit MSU.

Philip Kim visited Rice last week as one of our nanoscience-themed Chapman Lecturers, and it was great fun to talk science with him.  He gave two talks, the first a public lecture about graphene and the second a physics colloquium at a more technical level about how electrons in graphene act in many ways, like ultrarelativistic particles.  It was in this second talk that he gave the first truly clear explanation I've ever heard of the microscopic origin of the "pseudospin" description of carriers in graphene and what it means physically.  It got me thinking hard about the physics, that's for sure.

In the mean time, I spent yesterday visiting the Department of Physics and Astronomy at Michigan State.  They have a very good, enthusiastic condensed matter group there, with three hires in the last couple of years.  It was very educational for me, particularly learning about some of the experimental techniques that are being developed and used there.  Anyone who can measure resistances of 10^-8 Ohms to parts in 10⁵ gets respect!  Thanks to everyone who made the visit so nice.

Mars pictures

These pictures are stunning.  Wow!

Inspirational speech

I can't recall if I've posted this before.  If you're feeling down (e.g., because just about every story in the news today is horrifying to some degree), this might cheer you up.

3He

The lighter helium isotope, ³He, is not something that most people have ever heard of.  ³He is one neutron shy of the typical helium atom, and is present at a level of around 13 atoms per 10 million atoms of regular helium.  Every now and then there is some discussion out there in the sci-fi/futurist part of the world that we should mine the moon for ³He as a potential fuel for fusion reactors.  However, it turns out that ³He has uses that are much more down to earth.  

For example, in its pure form it can be used as the working fluid in an evaporative refrigerator.  Just as you cool off your tea by blowing across the top and allowing the most energetic water molecules to be carried away, it is possible to cool liquid helium by pumping away the gas above it.  In the case of regular ⁴He, the lowest temperature that you can reach this way ends up being about 1.1 K.  (Remember, helium is special in that at low pressures in bulk it remains a liquid all the way down as far as you care to go.)  This limit happens because the vapor pressure of ⁴He drops exponentially at very low temperatures - it doesn't matter how big a vacuum pump you have; you simply can't pull any more gas molecules away.  In contrast, ³He is lighter, as well as being a fermion (and thus obeying different quantum statistics than its heavier sibling).  This difference in properties means that it can get down to more like 0.26 K before its vapor pressure is so low that further pumping is useless.  (You don't throw away the pumped ³He.  You recycle it.)  This is the principle behind the ³He refrigerator.


You can do even better than that.  If you cool a mixture of ³He and ⁴He down well below 1 K, it will spontaneously separate into a ³He-rich phase (the concentrated phase, nearly pure), and a dilute phase of 6% ³He dissolved in 94% ⁴He.  At these temperatures the ⁴He is a superfluid, meaning that in many ways it acts like vacuum as far as the ³He atoms are concerned.  If you pump away the (nearly pure ³He) gas above the dilute phase, more ³He atoms are pulled out of the concentrated phase and into the dilute phase to maintain the 6% solubility.  This lets you evaporatively cool the concentrated phase much further, all the way down to milliKelvin temperatures.  (The trick is to run this in closed-cycle, so that the ³He atoms eventually end up back in the concentrated phase.)  This is the principle behind the dilution refrigerator, or "dil fridge".

Unfortunately, right now there is a major shortage of ³He.  Its price has shot up by something like a factor of 20 in the last year, and it's hard to get any at all.  This is a huge problem for a large number of (mostly) condensed matter physicists, as reported in the October issue of Physics Today (reprinted here (pdf)).  The reasons are complicated, but the proximate causes are an increase in demand (it's great for neutron detectors, which are handy if you're looking for nuclear weapons) and a decrease in supply (it comes from decay of tritium, mostly from triggers for nuclear warheads).  There are ways to fix this issue, but it will take time and cost money.  In the meantime, my sympathies go out to experimentalists who have spent their startups on fridges that they can't get running.