Optical Gaps and Excitonic Properties of 2D Materials by Hybrid Time-Dependent Density Functional Theory: Evidences for Monolayers and Prospects for van der Waals Heterostructures.

The optical properties of two-dimensional (2D) materials are accurately described by many-body methods including specifically pronounced electron-electron and electron-hole effects. Such methods are, however, computationally demanding and applicable on small computational cells only. We provide approximate optical gaps for 2D materials from time-dependent (TD) density functional theory based on a set of specific screened hybrid functionals and show that this approach effectively accounts for all important physical effects including excitons. Optical gap values obtained from the TD-HSE06 approach for a broad gap range 1-6 eV of eight 2D materials are in agreement with both experimental optical gaps and accurate GW+BSE calculations. Further, we show that such an approach is eligible and practicable for van der Waals heterostructures containing incommensurate cells of different monolayers and enables detailed analysis of intra- and interlayer excitonic wave functions. TD-HSE06 is therefore a suitable method for a reliable description of the optical properties of extended periodic 2D systems.