Topological bands in helical magnetic metals

In crystalline systems with a superstructure, energy bands can be non-periodic over the Brillouin zone yet form a gapless, periodic structure as a whole—a covering in topological terms. It is proved that the number of sheets in this covering and its monodromy are topological invariants under ambient isotopy. As a concrete manifestation of this nontrivial topology, we analyze three-sublattice models for 120°-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 a spin-textured, one-sheeted Fermi surface. The observable transport signatures of the topological metal and its potential experimental realization are briefly discussed.