  It has been recently predicted that the interplay between Coulomb
interactions and Berry curvature can produce interesting optical phenomena in
topologically nontrivial two-dimensional insulators. Here, we present a theory
of the optical absorption for three-dimensional, hole-doped Weyl semimetals. We
find that the Berry curvature, Coulomb interactions and the nonlinearity in the
single-particle energy spectrum can together enable a light-induced valley
polarization. We support and supplement our numerical results with an
analytical toy model calculation, which unveils topologically nontrivial Mahan
excitons with nonzero vorticity.
