  The Rashba-Dresselhaus effect is the splitting of doubly degenerate band
extrema in semiconductors, accompanied by the emergence of counter-rotating
spin textures and spin-momentum locking. Here we investigate how this effect is
modified by lattice vibrations. We show that, in centrosymmetric non-magnetic
crystals, for which a bulk Rashba-Dresselhaus effect is symmetry-forbidden,
electron-phonon interactions can induce a phonon-assisted, dynamic
Rashba-Dresselhaus spin splitting in the presence of an out-of-equilibrium
phonon population. In particular, we show how Rashba, Dresselhaus, or Weyl spin
textures can selectively be established by driving coherent infrared-active
phonons, and we perform ab initio calculations to quantify this effect for
halide perovskites.
