In crystalline systems with a superstructure, the electron dispersion can form a nontrivial covering of the Brillouin zone. 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.
@article{arxiv.2510.14784,
title = {Topological bands in metals},
author = {Yu. B. Kudasov},
journal= {arXiv preprint arXiv:2510.14784},
year = {2026}
}