I am trying to understand superconducting states of URu2Si2 where it is proposed that this heavy fermion compound has Weyl type superconducting states. So what are Weyl fermions and how are they relevant in finding the superconducting states of URu2Si2. For the reference, please see attached paper. Thanks
There are three different kinds of spin-1/2 particles: Dirac, Majorana, and Weyl.
The first, Dirac fermions, have non-zero mass, and are represented as four component complex spinors. This is the mathematical description of fermions which emerges naturally from the massive Dirac equation, which Paul Dirac invented to describe the electron, a massive spin-1/2 particle, relativistically.
Hermann Weyl showed that the massless Dirac equation could be reduced to a two-component equation. The solutions of that equation are called Weyl spinors, or Weyl fermions.
Weyl fermions are two-component spinors. They are irreducible representations of the Lorentz group, and since they are massless, their helicity is a good quantum number - it is boost invariant, since Weyl spinors move at the speed of light. So there is a well-defined notion of a left-handed or a right-handed Weyl spinor.
Massive Dirac spinors can be written as combinations of left and right handed massless Weyl fermions.
But there is another way of representing the massive Dirac equation found by Ettore Majorana, which makes its solutions into real four component spinors. Majorana fermions correspond to another possible type of four component spinor, which can have mass, called the Majorana mass. But the reality condition means that the particle is indistinguishable from the antiparticle for a Majorana fermion. The reality condition also means that Majorana spinors have a two component representation.
Both Weyl and Majorana spinors can be regarded as constrained cases of Dirac spinors.
Weyl fermions at first appeared to be the ones that were involved in the theory of the weak interactions. The particle is distinguishable from its anti-particle because the spinors are complex.
Majorana fermions on the other hand are four component spinors for which the particle and antiparticle are indistinguishable. A Majorana fermion is its own antiparticle - much like the neutral spin-1 photon. Massless Majorana fermions are the natural objects to act as partners to neutral spin-1 or spin-0 particles, for people who like to build supersymmetric theories.
At the current time, things are somewhat up in the air, since neutrinos have been found to be massive rather than massless - even if their masses are very small.
Here's a pretty nice didactic paper on the subject from arXiv:
http://arxiv.org/pdf/1006.1718v2...
Briefly, Weyl fermions are the two-component solutions of the Dirac equation for mass-less particles.
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