  Dirac semimetal is a phase of matter, whose elementary excitation is
described by the relativistic Dirac equation. In the limit of zero mass, its
parity-time symmetry enforces the Dirac fermion in the momentum space, which is
composed of two Weyl fermions with opposite chirality, to be non-chiral.
Inspired by the flavor symmetry in particle physics, we theoretically propose a
massless Dirac-like equation yet linking two Weyl fields with the identical
chirality by assuming SU(2) isospin symmetry, independent of the space-time
rotation exchanging the two fields. Dramatically, such symmetry is hidden in
certain solid-state spin-1/2 systems with negligible spin-orbit coupling, where
the spin degree of freedom is decoupled with the lattice. Therefore, the
existence of the corresponding quasiparticle, dubbed as flavor Weyl fermion,
cannot be explained by the conventional (magnetic) space group framework. The
four-fold degenerate flavor Weyl fermion manifests linear dispersion and a
Chern number of 2, leading to a robust network of topologically protected Fermi
arcs throughout the Brillouin zone. For material realization, we show that the
transition-metal chalcogenide CoNb3S6 with experimentally confirmed collinear
antiferromagnetic order is ideal for flavor Weyl semimetal under the
approximation of vanishing spin-orbit coupling. Our work reveals a counterpart
of the flavor symmetry in magnetic electronic systems, leading to further
possibilities of emergent phenomena in quantum materials.
