It's one of those cases where condensed matter physicists study a system which satisfies equations known from (more) fundamental theories. Other recurring examples are "black holes" in the lab [1] and "AdS/CFT" (of string theory fame) in solid state and quark-gluon plasma physics [2].
That aside, there is a mathematically well-defined sense in which Weyl fermions are the most "fundamental" fermions: the other kinds you hear about, Dirac and Majorana, can all be written as combinations of Weyl fermions. To make a Dirac, you take two Weyls of opposite helicity and couple them with a common mass term. To make a Majorana, you impose an additional algebraic condition on the two Weyls (take the complex conjugate of Weyl #2, reshuffle it a bit, and you get Weyl #1).
The most significant thing here is the mass term. When you look at the equations, it's immediately obvious that what the mass term does is mix the two Weyls in a Dirac: even if you prepare a pure state of one Weyl, as soon as you set the clock ticking, the mass term will turn it into a mix of two Weyls... unless the mass is exactly 0.
So a less mystifying way to describe the achievement of "making Weyl fermions" is simply "making massless fermions".
That aside, there is a mathematically well-defined sense in which Weyl fermions are the most "fundamental" fermions: the other kinds you hear about, Dirac and Majorana, can all be written as combinations of Weyl fermions. To make a Dirac, you take two Weyls of opposite helicity and couple them with a common mass term. To make a Majorana, you impose an additional algebraic condition on the two Weyls (take the complex conjugate of Weyl #2, reshuffle it a bit, and you get Weyl #1).
The most significant thing here is the mass term. When you look at the equations, it's immediately obvious that what the mass term does is mix the two Weyls in a Dirac: even if you prepare a pure state of one Weyl, as soon as you set the clock ticking, the mass term will turn it into a mix of two Weyls... unless the mass is exactly 0.
So a less mystifying way to describe the achievement of "making Weyl fermions" is simply "making massless fermions".
[1] http://www.nature.com/nphys/journal/v10/n11/full/nphys3104.h...
[2] https://en.wikipedia.org/wiki/AdS/CFT_correspondence#Applica...