Optical and transport properties of metals with nontrivial band geometry

I will describe how the geometry of the band structure of metals manifests itself in their optical and transport properties. In particular, I will discuss optical Hall response of chiral crystals in the presence of a DC transport current – the gyrotropic Hall effect – and show that it is related to the Berry curvature dipole. The latter fact makes the gyrotropic Hall effect a diagnostic tool for topological properties of three-dimensional chiral metals. I will also show how band geometry affects particle collisions by considering the anomalous Hall effect in the hydrodynamic regime.