Theory of band gap reduction due to conduction electrons in two-dimensional transition metal dichalcogenides: Imaginary frequency formalism

Two-dimensional transition metal dichalcogenides have a large direct band gap that shrinks with electron doping, with a sharp reduction at low density. Here, the authors develop the theory of band gap renormalization from many-body screening within the random phase approximation, where they consider full dynamical screening in the imaginary frequency domain. This method is analytically convenient and numerically accurate, with the results reproducing the low density $\ensuremath{\delta}\phantom{\rule{0}{0ex}}\mathcal{D}\ensuremath{\sim}{n}^{1/3}$ behavior expected from analysis of the self-energy integral, and agreeing well with available experimental data. This technique may be easily extended to other two dimensional semiconductors.