I recently read something about it in a national newspaper and I assume it's legit. I think Majorana fermions are fermions which are antiparticles of themselves and that might be why it has been so hard to get them.

The majorana fermions they found are a new variety of quasiparticle excitations in a superconductor. What is not legitimate is to draw any connection between these states and cosmology and/or dark matter.

It is important to note that the solid state manifestations of Majorana fermions are emergent low-energy localized modes of the system (quasiparticles) which are not fundamental new elementary particles as originally envisioned by Majorana (or as the neutrino would be if it turns out to be a Majorana fermion), but are effective linear combinations of half-electrons and half-holes which are topological anyonic objects obeying non-Abelian statistics. The terminology "Majorana fermion" is thus not a good nomenclature for these solid state Majorana modes.

In fact, if we define Majorana fermions as fermions that are identical to their antiparticle, then the quasi-particles in any superconductors will be Majorana fermions (even without vortex). This is because the quasi-particles in any superconductors are fermions that can annihilate with itself. Such kind of "Majorana fermion" (ie the one that is actually introduced by Majorana) has already been found in superconductors. What people are looking for recently is actually Majorana zero mode inside of a vortex or other defects of a superconductor. The Majorana zero mode, as a zero-dimensional object, does not have Bose/Fermi statistics as defined by exchange and braiding. A vortex that carries a Majorana zero mode has a non-Abelian statistics, which is also not a fermion. So the "Majorana zero modes" are very different from the Majorana fermions introduced by Majorana. Refering "Majorana zero modes" as "Majorana fermions" can be very confusing.

From my knowledge on this, whether neutrinos are Majorana or Dirac particles depends on the existence of the double beta neutrinoLESS decay.
If we observe it, then neutrinos are majorana particles, and that way our beloved conservations are not violated. Coz the 2 neutrinos that are emitted, annihilate each other (so the neutrino has to be its own antiparticle)