Topological skyrmion semimetals

We introduce topological skyrmion semimetal phases of matter, characterized by bulk electronic structures with topological defects in ground state observable textures over the Brillouin zone (BZ), rather than topological degeneracies in band structures. We present and characterize toy models for these novel topological phases, focusing on realizing such topological defects in the ground state spin expectation value texture over the BZ. We find generalized Fermi arc bulk-boundary correspondences and chiral anomaly response signatures, including Fermi arc-like states which do not terminate with topological band structure degeneracies in the bulk, but rather with topological defects in the spin texture of bulk insulators. We also consider novel boundary conditions for topological semimetals, in which the 3D bulk is mapped to a 2D bulk plus 0D defect. Given the experimental significance of topological semimetals, our work paves the way to broad experimental study of topological skyrmion phases and the quantum skyrmion Hall effect.