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Doped free carriers can substantially renormalize electronic self-energy andquasiparticle band gaps of two-dimensional (2D) materials. However, it is stillchallenging to quantitatively calculate this many-electron effect, particularlyat the low doping density that is most relevant to realistic experiments anddevices. Here we develop a first-principles-based effective-mass model withinthe GW approximation and show a dramatic band gap renormalization of a fewhundred meV for typical 2D semiconductors. Moreover, we reveal the roles ofdifferent many-electron interactions: The Coulomb-hole contribution is dominantfor low doping densities while the screened-exchange contribution is dominantfor high doping densities. Three prototypical 2D materials are studied by thismethod, h-BN, MoS2, and black phosphorus, covering insulators tosemiconductors. Especially, anisotropic black phosphorus exhibits asurprisingly large band gap renormalization because of its smallerdensity-of-state that enhances the screened-exchange interactions. Our workdemonstrates an efficient way to accurately calculate band gap renormalizationand provides quantitative understanding of doping-dependent many-electronphysics of general 2D semiconductors.

Renormalization of quasiparticle band gap in doped two-dimensional materials from many-body calculations