Skew band structure and anomalous conductivity of PdCrO$_2$

A model of magnetic interaction of CrO$_2$ and Pd hexagonal layers in PdCrO$_2$ is proposed. Since Cr-O-Pd bridges do not provide an interlayer magnetic coupling in case of a 120$^0$ magnetic ordering, a direct exchange interaction between magnetic chromium ions and conductive palladium layers is assumed. It is shown that this interaction leads to a novel state of itinerant electrons (skew bands). It is characterized by abnormally high conductivity at low temperatures due to strong suppression of umklapp electron-phonon scattering.