Semimetal with both Rarita-Schwinger-Weyl and Weyl excitations

A relativistic spinor with spin 3/2 is historically called Rarita-Schwinger spinor. The right- and left-handed chiral degrees of freedom for the massless Rarita-Schwinger spinor are independent and are thought of as the left- and right-Weyl fermion with helicity \pm3/2. We study three orbital spin-1/2 Weyl semimetals in the strong spin-orbital coupling limit with time reversal symmetry breaking. We find that in this limit the systems can be a J_{eff}=1/2 Weyl semimetal or a J_{eff}=3/2 semimetal, depending on the Fermi level position. The latter near Weyl points includes both degrees of freedom of Rarita-Schwinger-Weyl and Weyl's. A non-local potential separates the Weyl and Rarita-Schwinger-Weyl degrees of freedom and a relativistic Rarita-Schwinger-Weyl semimetal emerges. This recipe can be generalized to mulit-Weyl semimetal and Weyl fermions with pairing interaction and obtain high monopole charges. Similarly, a spatial inversion breaking Raita-Schwinger-Weyl semimetal may also emerge.