Electronic and Optical properties of transition metal dichalcogenides under symmetric and asymmetric field-effect doping

Doping via electrostatic gating is a powerful and widely used technique to tune the electron densities in layered materials. The microscopic details of how these setups affect the layered material are, however, subtle and call for careful theoretical treatments. Using semiconducting monolayers of transition metal dichalcogenides (TMDs) as prototypical systems affected by electrostatic gating, we show that the electronic and optical properties change indeed dramatically when the gating geometry is properly taken into account. This effect is implemented by a self-consistent calculation of the Coulomb interaction between the charges in different sub-layers within the tight-binding approximation. Thereby we consider both, single- and double-sided gating. Our results show that, at low doping levels of $10^{13}$ cm$^{-2}$, the electronic bands of monolayer TMDs shift rigidly for both types of gating, and subsequently undergo a Lifshitz transition. When approaching the doping level of $10^{14}$ cm$^{-2}$, the band structure changes dramatically, especially in the case of single-sided gating where we find that monolayer ce{MoS2} and ce{WS2} become indirect gap semiconductors. The optical conductivities calculated within linear response theory also show clear signatures of these doping-induced band structure renormalizations. Our numerical results based on light-weighted tight-binding models indicate the importance of electronic screening in doped layered structures, and pave the way for further understanding gated super-lattice structures formed by mutlilayers with extended Moir{e} pattern.