## Monday, July 27, 2015

### What are Weyl fermions? Do they really move charge 1000x faster?

A new paper (published online in Science) with experimental work from Zahid Hasan's group at Princeton has made a splash this week.  In it, they argue that they see evidence in crystals of the compound TaAs for (quasi)particles that have the properties of so-called Weyl fermions.  What does this mean?

I've written before about quasiparticles.  The idea is, in a big system of interacting  degrees of freedom (electrons for example), you can ask, how would we best describe the low energy excitations of that system?  Often the simplest, most natural description of the excitations involves entities with well-defined quantum numbers like momentum, angular momentum, electric charge, magnetic moment, and even something analogous to mass.  These low energy excitations are quasiparticles - they're "quasi" because they don't exist outside of the material medium in which they're defined, but they're "particles" because they have all these descriptive parameters that we usually think of as properties of material particles.  In this situation, when we say that a quasiparticle has a certain mass, this is code for a discussion about how the energy of the excitation depends upon its momentum.  For a non-relativistic, classical particle like a baseball, the kinetic energy $E = p^{2}/2m$, where $p$ is the magnitude of the momentum.  So, if a quasiparticle has an energy roughly quadratic in its momentum, we can look at the number in front of the $p^{2}$ and define it to be $1/2m^{*}$, where $m^{*}$ is an "effective mass".

In some materials under certain circumstances, you end up with quasiparticles with a kinetic energy that depends linearly on the momentum, $E \sim p$.  This is reminiscent of the situation for light in the vacuum, where $E = p c$, with $c$ the speed of light.  A quasiparticle with this "linear dispersion" is said to act like it's "massless", in the same way that light has no mass yet still has energy and momentum.  This doesn't mean that something in the material is truly massless - it just means that those quasiparticles propagate at a fixed speed (given by the constant of proportionality between energy and momentum).  If the quasiparticle happens to have spin-1/2 (and therefore is a fermion),  then it would be a "massless fermion".  It turns out that graphene is an example of a material where, near certain energies, the quasiparticles act like this, and mathematically are well-described by a formulation dreamed up by Dirac and others - these are "massless Dirac fermions".

Wait - it gets richer.  In materials with really strong spin-orbit coupling, you can have a situation where the massless, charged fermions have a spin that is really locked to the momentum of the quasiparticle.  That is, you can have a situation where the quasiparticles are either right-handed (picture the particle as a bullet, spinning clockwise about an axis along its direction of motion when viewed from behind) or left-handed.  If this does not happen only at particular momenta (or only at a material surface), but can happen over a more general energy and momentum range (and in the material bulk), these quasiparticles can be described in language formulated by Weyl, and are "Weyl fermions".   Thanks to their special properties, the Weyl particles are also immune to some back-scattering (the kind of thing that increases electrical resistance).  I'm being deliberately vague here rather than delving into the math.  If you are very motivated, this paper is a good pedagogical guide.

So, what did the authors actually do?  Primarily, they used a technique called angle-resolved photoemission spectroscopy (ARPES) to measure, in 3d and very precisely, the relationship between energy and momentum for the various quasiparticle excitations in really high quality crystals of TaAs.  They found all the signatures expected for Weyl fermion-like quasiparticles, which is pretty cool.

Will this lead to faster computers, with charge moving 1000x faster, as claimed in various mangled versions of the press release?  No.  I'm not even sure where the writers got that number, unless it's some statement about the mobility of charge carriers in TaAs relative to their mobility in silicon.    This system is a great example of how profound mathematical descriptions (formulated originally to deal with hypothetical "fundamental" high energy physics) can apply to emergent properties of many-body systems.  It's the kind of thing that makes you wonder how fundamental are some of the properties we see in particle physics.  Conceivably there could be some use of this material in some technology, but it is silly (and in my view unnecessary) to claim that it will speed up computers.

Anonymous said...

It is about the high mobility in these Weyl compounds.
A new paper by another group (Nature Physics 2015) in Germany confirms it.

An ultrahigh carrier mobility of 5 × 10^6 cm2 V−1 s−1 is reported for Weyl fermions.

B. Yan, et al.,
"Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP", Nature Physics, in press, DOI: 10.1038/nphys3372