Quasiparticle band-gap renormalization in doped monolayer MoS 2

The quasiparticle band-gap renormalization induced by the doped carriers is an important and well-known feature in two-dimensional semiconductors, including transition-metal dichalcogenides (TMDs), and it is of both theoretical and practical interest. To get a quantitative understanding of this effect, here we calculate the quasiparticle band-gap renormalization of the electron-doped monolayer ${\mathrm{MoS}}_{2}$, a prototypical member of TMDs. The many-body electron-electron interaction induced renormalization of the self-energy is found within the random phase approximation and to account for the quasi-2D character of the Coulomb interaction in this system a Keldysh-type interaction with a nonlocal dielectric constant is used. Considering the renormalization of both the valence and the conduction bands, our calculations reveal a large and nonlinear band-gap renormalization upon adding free carriers to the conduction band. We find a 410 meV reduction of the band gap for the monolayer ${\mathrm{MoS}}_{2}$ on ${\mathrm{SiO}}_{2}$ substrate at the free carrier density $n=4.9\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ which is in excellent agreement with available experimental results. We also discuss the role of exchange and correlation parts of the self-energy on the overall band-gap renormalization of the system. The strong dependence of the band-gap renormalization on the surrounding dielectric environment is also demonstrated in this work, and a much larger shrinkage of the band gap is predicted for the freestanding monolayer ${\mathrm{MoS}}_{2}$.