Competitive screening and band gap renormalization in n-type monolayer transition metal dichalcogenides

Gate induced carriers impact the many-body interactions in monolayer transition metal dichalcogenides (TMDs) by modifying the screened Coulomb potential and renormalizing the band gap, thus influencing the strong excitonic effects in these materials. Using the $GW$ approximation and a plasmon pole theory to model the carrier induced plasmons in the frequency-dependent part of the screening, we accurately calculate the band gap renormalization of the electron doped monolayer ${\mathrm{MoS}}_{2}$ and ${\mathrm{WS}}_{2}$. The excitonic states of the low doped systems are calculated by solving the Bethe-Salpeter equation. Our results clarify the competition between screening and band gap renormalization. An exact cancellation occurs between the reduced band gap and the exciton binding energy for doped monolayer ${\mathrm{WS}}_{2}$, in good agreement with previous experimental results. In contrast, the exciton energy of doped monolayer ${\mathrm{MoS}}_{2}$ blueshifts by tens of meV. We show the role of the electronic band structure of the monolayers in the calculated exciton energies. Our results could be generally expanded to other monolayer TMDs and are helpful for quantitatively engineering optoelectronic devices with desired features.