  We identify a Weyl semimetal state in an inversion breaking, stoichiometric
compound strontium silicide, SrSi$_2$, with many new and novel properties that
are distinct from the TaAs family. We theoretically show that SrSi$_2$ is a
Weyl semimetal even without spin-orbit coupling and that, after the inclusion
of spin-orbit coupling, two Weyl fermions stick together forming an exotic
double Weyl fermion with quadratic dispersions and a higher chiral topological
charge of 2. Moreover, we find that the Weyl nodes with opposite charges are
located at different energies due to the absence of mirror symmetry in
SrSi$_2$, leading to a unique topological quantum response that an external
magnetic field can induce a dissipationless current. Our systematic results not
only identify a much-needed robust Weyl semimetal candidate but also open the
door to new topological Weyl physics that is not possible in the TaAs family of
materials.
