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Graphene, topological insulators, and Weyl semimetals are three widelystudied materials classes which possess Dirac or Weyl cones arising from eithersublattice symmetry or spin-orbit coupling. In this work, we present a theoryof a new class of bulk Dirac and Weyl cones, dubbed Weyl orbital semimetals,where the orbital polarization and texture inversion between two electronicstates at discrete momenta lend itself into protected Dirac or Weyl coneswithout spin-orbit coupling. We also predict several families of Weyl orbitalsemimetals including V$_3$S$_4$, NiTi3S6, BLi, and PbO$_2$ via first-principleband structure calculations. We find that the highest Fermi velocity predictedin some of these materials is even larger than that of the existing Diracmaterials. The synthesis of Weyl orbital semimetals will not only expand theterritory of Dirac materials beyond the quintessential spin-orbit coupledsystems and hexagonal lattice to the entire periodic table, but it may alsoopen up new possibilities for orbital controlled electronics or `orbitronics'.

Theory of Weyl orbital semimetals and predictions of several materials classes