Fig. 3: Hybridization between intra- and interlayer excitons.

a Single-particle band structure of the WSe₂ BLs for θ = 60°, calculated by density functional theory (see Methods). After resonant excitation (red arrow) at the K point, electrons scatter via phonons (blue arrow) into the energetically favorable Λ valley to form hybrid excitons (X_hyb). b Within the microscopic model, the electron is located in a Λ-like valley of the top (Λ_top) or bottom (Λ_bot) layer for a finite crystallographic misalignment. The parabolic dispersion of intra- (E_intra) and interlayer (E_inter) excitons is shifted in momentum space by twisting the layers, owing to the momentum mismatch Δk between Λ_top and Λ_bot. Strong interlayer wavefunction overlap promotes electron hopping and exciton hybridization (pink glow). c The overlap (violet surface) of excitonic wavefunctions (blue and orange grids) in momentum space depends on Δk. For clarity, we only show the real part of the exciton wavefunctions. d Hybridization of 1s and 2p excitons lowers the energy levels (magenta lines) with respect to the corresponding non-hybridized states X_intra and X_inter (blue/orange lines). The situation is sketched for θ = 60°, θ = 50°, and θ = 0°. Zero energy is set to the non-hybridized 1s state at θ = 60°. The vertical black arrows mark respective 1s–2p transition energies.