Dirac Cones in Graphene, Interlayer Interaction in Layered Materials, and the Band Gap in MoS2

Ivan Yakovkin

doi:10.3390/cryst6110143

Abstract

The 2D outlook of graphene and similar layers has initiated a number of theoretical considerations of electronic structure that are both interesting and exciting, but applying these ideas to real layered systems, in terms of a model 2D system, must be done with extreme care. In the present review, we will discuss the applicability of the 2D concept with examples of peculiarities of electronic structures and interactions in particular layered systems: (i) Dirac points and cones in graphene; (ii) van der Waals interaction between MoS2 monolayers; and (iii) the issue of a 2D screening in estimates of the band gap for MoS2 monolayers.

Highlights

Layered systems have special properties which make them very promising in various applications such as nanoelectronics and catalysis [1,2,3,4,5,6,7,8]
The explanation for these phenomena was found with the help of the band structure calculations [12,13,14,15,16], which have revealed the transformation of the band gap from an indirect one for the bulk MoS2 to a direct one for the monolayer and an increase in the width of the band gap
We will discuss the applicability of the 2D concept with examples of peculiarities of electronic structures and interactions in particular layered systems: (i) Dirac points and cones in graphene (Section 2); (ii) van der Waals interaction between MoS2 monolayers (Section 3); (iii) screening and estimates of the band gap for MoS2 monolayer (Section 3)

Summary

Introduction

Layered systems have special properties which make them very promising in various applications such as nanoelectronics and catalysis [1,2,3,4,5,6,7,8]. A powerful technique of quantum electrodynamics and group theory has provided a detailed explanation of the peculiarities of the graphene electronic structure It should be mentioned, that the linear dispersion and EF band crossing at the K point were obtained from band structure calculations performed with one or another form of Schrödinger’s equation (for example, within DFT or tight-binding approximation), which afterwards were suggested to be invalid. We will discuss the applicability of the 2D concept with examples of peculiarities of electronic structures and interactions in particular layered systems: (i) Dirac points and cones in graphene (Section 2); (ii) van der Waals interaction between MoS2 monolayers (Section 3); (iii) screening and estimates of the band gap for MoS2 monolayer (Section 3).

Dirac Cones and Buckling in Graphene and Similar Layers

The Interlayer Interaction in Layered Crystals

Band Gap and Screening in MoS2 Layers

Conclusions