Floquet engineering of electronic states by light is a central topic in modern experiments. However, the impact of many-body interactions on the single-electron properties remains unclear in this nonequilibrium situation. We propose that interaction effects could be reasonably understood by performing perturbative expansion in both the pump field and the electron-electron interaction when computing physical quantities. As an example, we apply this approach to semiconductors and show analytically that excitonic effects, i.e., effects of electron-hole interaction, lead to dramatic corrections to the single-electron Floquet spectra even when the excitons are only virtually excited by the pump light. We compute these effects in phosphorene and monolayer ${\mathrm{MoS}}_2$ for time- and angle-resolved photoemission spectroscopy and ultrafast optical experiments.

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• Excitons
• Floquet systems
• Phosphorene
• Quantum many-body systems
• Many-body techniques
• Nonequilibrium Green's function
• Time & angle resolved photoemission spectroscopy