Topological bands in helical magnetic metals

In crystalline systems with a superstructure, the electron dispersion canform a nontrivial covering of the Brillouin zone. It is proved that the numberof sheets in this covering and its monodromy are topological invariants underambient isotopy. As a concrete manifestation of this nontrivial topology, weanalyze three-sublattice models for 120$^\circ$-ordered helimagnets in one,two, and three dimensions. The two-dimensional system exhibits unconventional$f$-wave magnetism and a specific topological metal state characterized by aspin-textured, one-sheeted Fermi surface. The observable transport signaturesof the topological metal and its potential experimental realization are brieflydiscussed.