Topological bands in metals with helical magnetic order

The effect of a helicoidal magnetic field on the dispersion of conduction electrons in one- and two-dimensional systems is investigated. In a helicoidal periodic magnetic field, there is a special symmetry with respect to the reversal of time, which leads to the peculiarities of the band structure. Using an example of a one-dimensional model system, the topological properties of the band structure in an effective magnetic field corresponding to the 120$^\circ$-ordering are investigated. In PdCrO$_2$, the 120$^\circ$ magnetic ordering of the dielectric layers of CrO$_2$ creates an unusual spin structure of the Fermi surface in conducting palladium layers. In this case, the umklapp scattering of mobile charge carriers is strongly suppressed, which leads to abnormally high conductivity at low temperatures observed experimentally.