Dirac and Weyl Superconductors in Three Dimensions

We introduce the concept of 3D Dirac (Weyl) superconductors (SC), which have protected bulk four(two)-fold nodal points and surface Andreev arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry, e.g., the nodal phases of Cu$_x$Bi$_2$Se$_3$. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken. A Dirac node may split into a pair of Weyl nodes, only when time-reversal symmetry is broken.