A new type of Weyl semimetal with quadratic double Weyl fermions in SrSi2

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.