## Thursday, July 12, 2012

### Exotic (quasi)particles, and why experimental physics is challenging

There was a very large amount of press, some of it rather breathless, earlier in the year about the reported observation of (effective) Majorana fermions in condensed matter systems.  Originally hypothesized in the context of particle physics, Majorana fermions are particles with rather weird properties.  Majorana looked hard at the Dirac equation (which is complex), and considered particles "built out of" linear combinations of components of solutions to the Dirac equation.  These hypothesized particles would obey a real (not complex) wave equation, and would have the rather odd property that they are their own antiparticles (!)  In the language of quantum field theory, if the operator $\gamma^{\dagger}$ creates a Majorana particle, then $\gamma^{\dagger} \gamma^{\dagger}$ creates and destroys one, leaving behind nothing.  In the context of condensed matter, it has been theorized (here and here, for example) that it's possible to take a superconductor and a semiconductor wire with strong spin-orbit coupling, and end up with a composite system that has low energy excitations (quasiparticles) that have properties like those of Majorana fermions.

So, if you had these funky quasiparticles in your system, how could you tell?  What experiment could you do that would give you the relevant information?  What knob could you turn and what could you measure that would confirm or deny their presence?  That's the challenge (and the fun and the frustration) of experimental physics.  There are only so many properties that can be measured in the lab, and only so many control parameters that can be tuned.  Is it possible to be clever and find an experimental configuration and a measurement that give an unambiguous result, one that can only be explained in this case by Majorana modes?

In the particular experiment that received the lion's share of attention, the experimental signature was a "zero-bias peak" in the electrical conductance of these structures.  The (differential) conductance is the slope of the $I-V$ curve of an electrical device - at any given voltage (colloquially called "bias"), the (differential) conductance tells you how much more current you would get if you increased the voltage by a tiny amount.  In this case, the experimentalists found a peak in the conductance near $V = 0$, and that peak stayed put at $V = 0$ even when a magnetic field was varied quite a bit, and a gate voltage was used to tune the amount of charge in the semiconductor.  This agreed well with predictions for the situation when there is a Majorana-like quasiparticle bound to the semiconductor/superconductor interface.

The question is, though, is that, by itself, sufficient to prove the existence of Majorana-like quasiparticles experimentally?  According to this new paper, perhaps not.  It looks like it's theoretically possible to have other (boring, conventional) quasiparticles that can form bound states at that interface that also give a zero-bias peak in the conductance.  Hmm.  Looks like it may well be necessary to look at other measurable quantities besides just the conductance to try to settle this once and for all.  This is an important point that gets too little appreciation in popular treatments of physics.  It's rare that you can directly measure the really interesting property or system directly.  Instead, you have to use the tools at your disposal to test the implications of the various possibilities.

Ross H. McKenzie said...

Hi Doug,

Thanks for the nice post.

First, I think this subtle issue [necessary vs. sufficient conditions] does not get enough attention by the science community, not just in popular treatments. A prominent case is that of quasi-crystals. People failed to appreciate that periodic order was a sufficient but not a necessary condition for the existence of discrete diffraction peaks.

Second, this post also highlights why good theory is so challenging! It is very hard for theorists to propose experiments that can definitively test their theories.

Igor said...

Here's another paper questioning Majorana's in ZBCP from P. Lee's group: http://arxiv.org/abs/1206.1276

Unknown said...

My friends in Station Q have mentioned this paper to me (doubting Majorana fermions), but they aren't so sure about whether the argument carries through.

http://arxiv.org/abs/1206.0434