Figure 1.

Schematics of the Dirac semimetal (DSM) and flavor Weyl semimetal (flavor WSM)

(A) A Dirac point can be viewed as the superposition of two Weyl points with opposite chirality in a DSM. Such superposition is generally obtained by the space-time $PT$ symmetry.

(B) The surface states of the DSM are adiabatically connected to topologically trivial surface states. The green points denote the Dirac points.

(C) A flavor WSM hosts 4-fold degenerate points composed of two Weyl points with identical chirality, protected by a hidden $SU\left(2\right)$ symmetry group (analogous to the isospin symmetry in particle physics).

(D) The surface states of flavor WSM are robust owing to the protection of chiral charges. The surface states on the surfaces that preserve the $SU\left(2\right)$ symmetry are 2-fold degenerate connecting two flavor Weyl points with opposite chirality. However, the surface states on the surfaces with a broken $SU\left(2\right)$ symmetry group split into two spin-polarized branches, resembling conventional topological insulators or semimetals.