Fig. 2: Evolution of the 1s–2p resonance with interlayer twist angle.

a, b Pump-induced changes of the real parts of the optical conductivity Δσ₁ (a) and the dielectric function Δε₁ (b) for a fixed pump-probe delay time t_pp = 5.1 ps as a function of the photon energy for samples with different twist angles θ. The blue spheres represent the dielectric response measured for the photoexcited WSe₂ BLs (pump fluence Φ = 27 µJ cm⁻²; sample temperature, 5 K). The blue shaded areas indicate the fits to the experimental data by a phenomenological model (see Methods). The dashed line and the blue/red arrow indicate the blue/red shift of the intraexcitonic 1s–2p resonance energy for increasing misalignment angle with respect to the 2H stacking. c Intraexcitonic 1s–2p transition energy ħω_res (black spheres) extracted from the data in a, b and derived from the microscopic theory (blue circles) as function of the twist angle θ. For θ = 21° and θ = 30°, microscopic calculations of hybrid excitons were not feasible. In the case of θ = 0°, the intraexcitonic resonance exhibits a strong dependence on the exciton density (see Fig. 4c and Supplementary Note 4). The gray sphere indicates the resonance energy as obtained for a pump fluence of Φ = 7 µJ cm⁻², yielding the best agreement with the microscopic theory. The error bars represent the 95% confidence interval of the fitting procedure.