  We study a class of Dirac semimetals that feature an eightfold-degenerate
double Dirac point. We show that 7 of the 230 space groups can host such Dirac
points and argue that they all generically display linear dispersion. We
introduce an explicit tight-binding model for space groups 130 and 135, showing
that 135 can host an intrinsic double Dirac semimetal -- one with no additional
degeneracies at the Fermi energy. We consider symmetry-lowering perturbations
and show that uniaxial compressive strain in different directions leads to
topologically distinct insulating phases. In addition, the double Dirac
semimetal can accommodate topological line defects that bind helical modes.
Potential materials realizations are discussed.
