Zoo of Nodal-loop Metals

Topological states of matter have been attracting great interest. Following the studies on topological insulators, the recent focus shifts towards the various topological metals (or semimetals), in which nontrivial band crossings appear near the Fermi level, endowing the low-energy electrons with novel emergent properties. In this talk, I discuss a class of metals where the band crossings form 1D loops in the Brillouin zone. I show that the loops can be characterized by several properties. Depending on how the loop winds around the Brillouin zone, it has a Z^3 characterization. The type of dispersion around the loop classifies the loop into type-I, type-II, or the hybrid type. The type-II loop shows suppressed low-frequency optical absorption, and the hybrid loop shows zero-field magnetic breakdown and distinct features in the magnetic quantum oscillations. Under spin-orbit coupling, some loops are gapped out, but some are robust owing to certain nonsymmorphic symmetries. Under proper conditions, multiple loops can exist, connect each other, and form a nodal chain.