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

Abstract

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.

Optical gaps and excitons in semiconducting transition metal carbides (MXenes)

“…33 Furthermore, we compute the optical absorption spectrum using TD-DFT along with the HSE06 hybrid functional. 25,34 The basic idea of this TD-HSE06 method is to replace the local exchange-correlation kernel by a non-local one. Then the optical absorption spectrum can be computed by solving the Casida's equation.…”

“…Then the optical absorption spectrum can be computed by solving the Casida's equation. According to our recent work, 25 the matrix equation in the TD-HSE06 method is similar to the BSE but the screened interaction W is replaced by one-quarter of the non-local screened exchange term with a fixed screening parameter o. The TD-HSE06 method makes it possible to describe excitons in the optical spectra and can be regarded as an approximation of the BSE with the perfect accuracy for the 2D materials.…”

“…The TD-HSE06 method makes it possible to describe excitons in the optical spectra and can be regarded as an approximation of the BSE with the perfect accuracy for the 2D materials. 25 After computing the energy-dependent dielectric function (a broadening of 0.1 eV is used), we can determine the actual optical absorbance that can be written as 35…”

“…Our previous investigation has shown that the k-point grid affects the accuracy of the absorbance spectra significantly. 25 The optimal values of the other parameters including the cut-off energy and the number of bands have been determined and we also use the optimal parameters found in ref. 25 in this work.…”

“…We have shown recently that this approach (TD-HSE06) is very successful for a broad set of 2D materials. 25 In addition, TD-DFT together with the so-called Bootstrap kernel has been shown to be a suitable method for describing the excitonic properties of 2D materials qualitatively. 26,27 The goal of our work is to provide reasonable optical gaps and absorbance spectra for various semiconducting MXenes using the TD-HSE06 method.…”