The interlayer exciton ($IL$) in bilayer $2H\text{−}{\mathrm{MoS}}_2$ has earlier been shown to undergo large Stark splitting under electric field $F_z\parallel \mathbf{c}$ axis. We show that the excited state exciton $A_{2s}$ in bulk $2H\text{−}{\mathrm{MoS}}_2$ undergoes nearly three times as large splitting, with a dipole moment magnitude 1.46 enm. The nature and evolution of different exciton species with $F_z$ is verified by comparison with ab initio GW-Bethe-Salpheter equation (BSE) calculations that include the full electron-hole correlations. The excitonic wave functions reveal the individual character of the exciton states at high $F_z$ as the ground state $A_{1s}$, split interlayer $I{L}_{-}, I{L}_{+}$, and split excited state $A_{2s-}$. Extrapolation to low $F_z$ indicates that $IL$ and $A_{2s}$ mix strongly. We try to rationalize the large dipole moment values by comparing GW-BSE results with the hydrogenic exciton model. Although the dominant $A_{1s}$ shows an insignificant Stark shift, its large anticrossing with $A_{2s-}$ provides a pathway for its modulation and control using an electric field.

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• Bethe-Salpeter equation
• Excitons
• Layered crystals
• Transition metal dichalcogenides
• Density functional theory
• First-principles calculations
• Reflectivity