In much of the literature floating around, it is commonly implied that an important part of obtaining a Weyl semimetal phase is to break either time reversal symmetry or inversion symmetry.
However, none of the literature I found seems to give a clear answer on why these symmetries seem mutually exclusive in Weyl semimetals, it is just taken for granted that you can't break both symmetries.
Why is this assumed?
I had thought that all these broken symmetries did was to lift the spin or sublattice degeneracy, which in principle should still permit a Weyl node pair.
Is there something that forces a gap to appear when inversion and time reversal symmetries are broken?