Following their insulating counterparts, topological semi-metals have attracted much theoretical and experimental interest. Weyl semimetals in particular have been theoretically predicted and experimentally observed; they display topologically protected Fermi-arc surface states, as well as large negative magnetoresistance due to the “chiral anomaly.” In this talk, I will show how topologically charged fermions generically emerge in chiral crystal structures. Beyond Weyl semimetals, I will show how crystal symmetries can stabilize multifold fermions in both magnetic and nonmagnetic systems. I will discuss some notable consequences of these degeneracies such as the presence of multiple fermi arcs, and approximately quantized nonlinear optical response, which have been seen in recent experiments.
