  Graphene, topological insulators, and Weyl semimetals are three widely
studied materials classes which possess Dirac or Weyl cones arising from either
sublattice symmetry or spin-orbit coupling. In this work, we present a theory
of a new class of bulk Dirac and Weyl cones, dubbed Weyl orbital semimetals,
where the orbital polarization and texture inversion between two electronic
states at discrete momenta lend itself into protected Dirac or Weyl cones
without spin-orbit coupling. We also predict several families of Weyl orbital
semimetals including V$_3$S$_4$, NiTi3S6, BLi, and PbO$_2$ via first-principle
band structure calculations. We find that the highest Fermi velocity predicted
in some of these materials is even larger than that of the existing Dirac
materials. The synthesis of Weyl orbital semimetals will not only expand the
territory of Dirac materials beyond the quintessential spin-orbit coupled
systems and hexagonal lattice to the entire periodic table, but it may also
open up new possibilities for orbital controlled electronics or `orbitronics'.
