Generalized Bloch theorem and band-structure topology

Dispersion relations in a metal with a commensurate helical magnetic order are considered in the framework of one- and two-dimensional tight-binding models. The generalized Bloch theorem for translations combined with spin rotations, together with the Born–Karman periodic boundary conditions, leads to the appearance of multisheet dispersion curves (surfaces). It is demonstrated that the resulting band structure is topologically nontrivial, which can lead to a spin textured Fermi surface and cause transport anomalies.