Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals

In this talk, I present our recent study about electronic transport in Weyl semimetals with spatially varying nodal tilt profiles. We discuss two complementary approaches that characterise the electron flow: solutions of the semi-classical equations of motion, in analogy to those encountered in black hole spacetimes, and large-scale microscopic simulations of a scattering region surrounded by semi-infinite leads. We show that the two approaches lead to equivalent results when the wave packet is sufficiently far from the center of the tilt. The two methods are arguably a powerful toolset in the pursuit of tilt-tronic devices such as e.g. electronic lenses.