Sunday, July 23, 2017

Several items - the arxiv, "axial-gravitational" fun, topology

Things have been a bit busy, but here are a few items that have popped up recently:
  • Symmetry magazine is generally insightful and well-written.   Recently they posted this amusing article looking at various fun papers on the arxiv.  Their first example reminds me of this classic.
  • Speaking of the arxiv, it's creator, Paul Ginsparg, posted this engaging overview recently.  It's not an overstatement to say that the arxiv has had an enormous impact on science over the last 25 years.
  • There has been a huge amount of media attention on this paper (arxiv version).  The short version:  In high energy physics there is a certain conservation principle regarding chiral (meaning that the particle spin is directed along its momentum) massless fermions, so that ordinarily these things are produced so that there is no net excess of one handedness of spin over the other.  There is a long-standing high energy theory argument that in curved spacetime, the situation changes and you can get an excess of one handedness - a "chiral anomaly".  It is difficult to see how one could test this directly via experiment, since in our daily existence spacetime curvature is pretty minimal, unlike, say, near the event horizon of a small blackhole.  However, solid state materials can provide a playground for some wild ideas.  The spatial arrangement of atoms in a crystalline solid strongly affects the dispersion relation, the relationship between energy and (the crystal analog of) momentum.  For example, the linear dispersion relation between energy and momentum in (neutral) graphene makes the electrons behave in some ways analogous to massless relativistic particles, and lets people do experiments that test the math behind things like Klein tunneling.  As a bonus, you can add in spin-orbit coupling in solids to bring spin into the picture.  In this particular example, the electronic structure of NbP is such that, once one accounts for the spatial symmetries and spin-orbit effects, and if the number of electrons in there is right, the low-energy electronic excitations are supposed to act mathematically like massless chiral fermions (Weyl fermions).  Moreover, in a temperature gradient, the math looks like that used to describe that gravitational anomaly I'd mentioned above, and this is a system where one can actually do measurements.  However, there is a lot of hype about this, so it's worth stating clearly:  gravity itself does not play a role in NbP or this experiment.  Also, I have heard concerns about the strength of the experimental interpretation, because of issues about anisotropy in the NbP material and the aspect ratio of the sample.  
  • Similarly, there is going to be a lot of media attention around this paper, where researchers have combined a material ((Cr0.12Bi0.26Sb0.62)2Te3) that acts like a kind of topological insulator (a quantum anomalous Hall insulator, to use the authors' particular language) and a superconductor (Nb).  The result is predicted to be a system where there is conduction around the edges with the low energy current-carrying excitations act like Majorana fermions, another concept originally invented in the context of high energy physics.  
  • Both of these are examples of a kind of topology mania going on in condensed matter physics these days, as described here.  This deserves a longer discussion later.  


Anonymous said...

Could you elaborate on the interpretation issues in the NbP experiment? I notice that the paper doesn't mention phonon drag at all, which is very concerning since to the best of my knowledge that is one of the things that made such measurements difficult in GaAs.

Douglas Natelson said...

Caveat: I haven't read the paper extremely closely. One issue, often present in these topologically interesting materials, is where the Fermi level sits in the NbP, which affects whether the accessible carriers are Weyl-like or not. A second issue, which I did not know about until I was directed to this paper, is "current jetting". In some materials, there can be an enormous transverse magnetoresistance, so that the current ends up flowing in a very narrowly defined path, and that can affect interpretation of measurements unless sample geometry is chosen very carefully. Again, this is not my speciality; perhaps a reader more focused on that topic can say something clearer.