In most scenarios, Weyl fermions are considered massless, but this depends on the context and the specific conditions. In particle physics, the concept of Weyl fermions is often associated with the massless chiral fermions that emerge as low-energy excitations in certain topological materials, such as Weyl semimetals. In this context, Weyl fermions behave as particles with zero mass and possess a unique band structure characterized by a linear dispersion relation. However, it's worth noting that Weyl fermions can acquire a non-zero mass under specific circumstances.

Massless Weyl fermions arise as a consequence of certain symmetries in the underlying Hamiltonian of the material. These symmetries protect the Weyl nodes (the points in the band structure where the valence and conduction bands touch) and ensure that the fermions near these nodes behave as massless particles. However, these symmetries can be broken, either spontaneously or explicitly, which can lead to a non-zero mass for the Weyl fermions.

One scenario where Weyl fermions can acquire a non-zero mass is through the spontaneous breaking of a continuous symmetry, such as time-reversal symmetry. This can occur, for example, in the presence of magnetic order or certain types of structural distortions. When this symmetry is broken, the two Weyl nodes of opposite chirality can split in energy, resulting in a mass gap and a finite mass for the Weyl fermions.

Another scenario where Weyl fermions can become massive is through the explicit breaking of a discrete symmetry, such as inversion symmetry. This can happen, for example, in the presence of external electric fields or certain types of interfaces or boundaries. When this symmetry is broken, the Weyl nodes of opposite chirality can mix and hybridize, leading to a non-zero mass for the resulting quasiparticles.

In summary, while Weyl fermions are often described as massless in the context of topological materials, their actual mass status depends on the specific symmetries and conditions present in the system. Under certain circumstances, such as the breaking of certain symmetries, Weyl fermions can acquire a non-zero mass.