Semimetal with both Rarita-Schwinger-Weyl and Weyl excitations

A relativistic spinor with spin 3/2 is historically called a 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 fermions with helicity +/- 3/2. 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 degrees of freedom of both Rarita-Schwinger-Weyl and Weyl. A nonlocal 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 a mulit-Weyl semimetal and Weyl fermions with pairing interaction to obtain high monopole charges. Similarly, a spatial-inversion-breaking Raita-Schwinger-Weyl semimetal may also emerge.