Theory of Band Gap Reduction Due to Conduction Electrons in 2D TMDs: Imaginary Frequency Formalism

Abstract: Two Dimensional (2D) Transition Metal Dichalcogenides (TMDs) possess a large direct band gap which has been experimentally observed to shrink with increasing charge carrier density (doping). The effect has been the subject of theoretical study in recent years using various approaches and approximations. In this work we develop the theory of bandgap renormalization based on Feynman diagrammatic technique in the imaginary frequency formalism. We consider dynamical screening from conduction band electrons using the random phase approximation (RPA), as well as screening from a metallic gate. While our theory is general for any 2D semiconductor, to be specific we consider MoS$_2$ and WSe$_2$ and compare with available experimental data. In both cases we calculate large band gap renormalization that reaches several hundred meV at relatively low carrier density. This is in good agreement with experimental data.