The number of sheets and monodromy of the electron dispersion covering of the Brillouin zone in superstructured crystals are topological invariants, realized in three-sublattice helimagnet models as a spin-textured one-sheeted Fermi surface in a topological metal.
Tkachev, Topological Insulators, The Physics of Spin Helicity in Quantum Transport (Taylor & Francis Group, LLC, 2016)
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Topological bands in metals
The number of sheets and monodromy of the electron dispersion covering of the Brillouin zone in superstructured crystals are topological invariants, realized in three-sublattice helimagnet models as a spin-textured one-sheeted Fermi surface in a topological metal.