Fig. 4: Control over core-exciton screening with carrier density and distribution.

a Computed change in core-exciton binding energy (ΔE_b) as a function of excitation density with respect to the equilibrium exciton binding energy (734 meV). b Evolution of the integrated XTA amplitude as a function of excitation fluence over the energy ranges 9.658–9.664 keV (red circles), 9.664–9.669 keV (blue circles), and 9.670–9.673 keV (green circles). The shaded areas represent confidence intervals based on the integration of the XTA amplitude within one standard deviation. Linear fittings are weighted by the confidence intervals and constrained to fluences <50 mJ cm⁻². Details of the experimental excitation density calculation in Supplementary section 8, fluence dependence data in Supplementary section 9. c Computed integral of the normalized XTA amplitude using the cDFT+BSE method as a function of excitation density over the same energy range and color coding. Lines are linear fits constrained to excitation densities between 2 × 10¹⁹ cm⁻³ and 1 × 10²⁰ cm⁻³, showing the sub-linearity of the calculated XTA amplitude. b, c colored arrows show the interpolated amplitude at zero excitation density from the linear fits. Residuals of the linear fits are in the lower panels. d–f Distributions of photoexcited electrons (red circles) and holes (green circles) over (d) 1, (e) 3, and (f) 5 k-points at a fixed excitation density of 5.0 × 10¹⁹ cm⁻³. The area of the circles is proportional to the occupation at a given k-point. g Computed XTA spectra with cDFT+BSE for the different carrier distributions in (d–f) with the same color coding.