Chern numbers and nodal points in topological semi metals.

Nonmagnetic topological materials have dominated the landscape of topological physics for the past two decades. These breakthroughs in non-magnetic materials have not yet been matched by similar advances in magnetic compounds. Using magnetic band theory and topological indices obtained from Magnetic Topological Quantum Chemistry (MTQC), I will present a systematic way of identifying magnetic topological materials. I will then, focus on high order magnetic semimetals, and provide a topological classification of different fermions in these phases. Finally I will present new experimental realizations in materials. In particular I will focus on the pyrite compound CoS2, using complementary bulk- and surface-sensitive angle-resolved photoelectron spectroscopy and ab-initio calculations we discovered Weyl-cones at the Fermi-level and we directly observed the topological Fermi-arc surface states that link the Weyl-nodes, which will influence the performance of CoS2 as a spin-injector by modifying its spin-polarization at interfaces.
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