Fig. 3: Light-driven carrier energy shifts from self-energy perspective.

a Energy bands and the excitonic 1A₁ state in the absence of an electric field. b Field-induced renormalization of excitonic and Bloch states. Charge carrier transitions in the presence of a strong, non-resonant electric field result in population-dependent excitonic energy shift (ΔE_XS) due to the Stark effect, band edge shift (ΔE_FK), and density of state oscillations due to dynamical Franz-Keldysh effect, as well as the ponderomotive effect (Up) within the continuum of Bloch states. The colors (red and blue) of the arrows correspond to the energy shifts. c An analytic result for the delay-dependent electron energy shifts derived from the dynamics described in the panel. In negative time delays, when the carriers are in the ground state, the redshift is caused by the excitonic AC Stark and dynamical Franz-Keldysh effects. For positive time delays, the field-induced virtual transitions between the excitonic and Bloch states as well as the ponderomotive effect, contribute to the excited carrier energies and induce a blueshift. The light blue and red lines represent the low and high pump conditions, respectively.