Majorana Fermions, Retracted
Physics uses math, particle physics in particular. The complex numbers are a great entry point to studying these ideas. The complex numbers are like the “real” numbers we’re all familiar with, but also include the square root of minus one. And while that might seem abstract, these more complicated numbers are physical! They play an important role in quantum mechanics and also in modeling the electric charge.
Charged particles like protons or electrons come in antiparticle pairs: those with positive and negative electric charge. While complex numbers comes complex conjugation, which naturally models these pairs of particles.
Electrically neutral particles - like the neutron or even atoms - are actually composed electrically charged particles, and so also use those complex numbers. Of course, not all particles have complex pairs. The photon - the particle of light - is a boson based on real numbers.
One mystery that remains in physics is the possibility of a “real” fermion. Fermions are particles like electrons or protons, they’re things that take up space and have mass. To date, all observed fermions are “complex”; none are real. The ghostly neutrino is one such candidate, and those experiments are currently underway.
Neutrinos are fundamental particles, but not all particles are “fundamental”. Atoms are a great example of a composite particle. “Holes” in semiconductors are another kind of example: they are the literal absence of electrons. These days, there’s a whole zoo of “quasiparticles” in modern materials.
Just as complex numbers decompose to their real and imaginary parts, so too can complex fermions. And they don’t always separate in the way you’d expect. Theoretical calculations predict that a combination of an electron and a “hole” can separate, quantum mechanically, into “half-electron/half-hole” pairs.
If found, such a half-electrons/half-hole quantum excitation of the electric structure of graphene would be modeled by a real fermion, otherwise known as a Majorana particle. (Note that Majorana here is something of a taxonomic label, a “genus” of particle, rather than a specific species)
Modifying graphene - a one-atom thick layer of graphite - was a promising medium to find the elusive Majorana fermion. And recently, such an observation was claimed! Until it wasn’t. Those folks who claimed discovery retracted their recent paper.
Science is messy.
The race to observe one is likely a race for the Nobel prize. To quote Thomas Lewton’s recent article quoting condensed matter physicist Sankar Das Sarma - “I guarantee you the Majorana [fermion] will be seen, because its theory is pristine. This is an engineering problem; this is not a physics problem,” he said.
