Question

Are broken time reversal symmetry and inversion symmetry forbidden in a Weyl semimetal?

Answer 1

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.
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Answer 2

HEY MATE ⭐⭐⭐
HERE IS THE ANSWER ✌
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.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.

all these broken symmetries did was to lift the spin or sublattice degeneracy, which in principle should still permit a Weyl node pair.

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HOPE IT HELPS ☺☺☺