Figure 2. Out-of-plane spatial sensitivity of environmental screening.

(a) Experimentally and theoretically obtained energy separation Δ₁₂ between the n=1 and n=2 exciton states as a function of the number of layers of capping graphene. Dashed lines indicate Δ₁₂ values from the solution of the electrostatic model for uncapped WS₂ supported by fused silica substrate (grey) and covered with bulk graphite (red), representing two ideal limiting cases. (b) Absolute energies of the experimentally measured exciton ground state (n=1) and the first excited state (n=2) resonances, as well as the estimated positions of the bandgap obtained by adding the exciton binding energy to the energy of the n=1 state. The binding energy scales with Δ₁₂, where the limiting cases are an experimentally determined non-hydrogenic scaling for WS₂ on SiO₂ substrate from ref. 24 and the 2D-hydrogen model in a homogeneous dielectric . These are compared to the bandgap energies deduced from the calculated exciton binding energies using the QEH model. The solid lines are guides to the eye.