arXiv:1107.0600v1 [cond-mat.mtrl-sci] 4 Jul 2011 Large Excitonic Effects in the Optical Properties of Monolayer MoS 2 Thomas Olsen, Karsten W. Jacobsen, and Kristian S. Thygesen ∗ Center for Atomic-Scale Materials Design, Department of Physics, Technical University of Denmark, DK–2800 Kongens Lyngby, Denmark (Dated: July 5, 2011) The band structure and absorption spectrum of monolayer MoS2 is calculated using the G0W0 approximation and the Bethe-Salpeter equation (BSE), respectively. We find that the so-called A and B peaks in the absorption spectrum arise from strongly bound excitons (0.7-0.8 eV) localized in distinct regions of the Brillouin zone and not from a split valence band as commonly assumed. Furthermore, we find the minimum band gap to be of the indirect type. This seems to conflict with recent experimental results showing stong luminescence in this material. However, our results indicate that the luminescence is a consequence of the large binding energy of the lowest exciton which stabilizes it against thermal relaxation. PACS numbers: 71.20.Nr, 71.35.-y, 73.22.-f, 78.20.Bh, 78.60.Lc Nanostructured forms of the semi-conductor MoS 2 have recieved much attention due to their potential as catalysts for desulferization of crude oil and more re- cently for (photo)-electrochemical hydrogen evolution[1– 3]. Bulk MoS 2 is composed of two-dimensional sheets held together by weak van der Waals forces and indi- vidual sheets can be isolated by exfoliation techniques similar to those used to produce graphene[4]. Single lay- ers of MoS 2 therefore comprise highly interesting two- dimensional systems with a finite band gap and have re- cently been proposed for nano-electronics applications[5]. The optical properties of MoS 2 have been thoroughly studied experimentally [6–11]. The absorption spectrum shows two distinct low energy peaks at 1.88 eV and 2.06 eV , which are denoted by A and B respectively [12]. These features have traditionally been proposed to origi- nate from direct transitions between a split valence band and the conduction band at the K point of the Brillouin zone. Their Rydberg satellites, Zeeman splitting, and dependence on crystal thickness have been investigated in detail [9]. Very recently, the quantum yield of lumi- nescence from MoS 2 was shown to increase dramatically when the sample thickness was changed from a few lay- ers to a monolayer [13, 14] and the results have been taken as an indication of a direct band gap in the single layer. This conjecture is supported by density functional theory (DFT) calculations, which indeed show a transi- tion from indirect to direct gap when going from a few layers to monolayer MoS 2 [14–16]. However, while DFT has proven very successful in describing the ground state properties of a large variety of materials, it is not ex- pected to provide a faithful description of excited state properties such as optical absorption and luminescence. In this letter we present first-principles many-body perturbation theory calculations for the electronic struc- ture of MoS 2 . We show that monolayer MoS 2 has an indirect gap at the K − T transition, which is ∼ 0.5 eV smaller than the direct gap at K. The experimental ab- sorption spectrum is reproduced by our calculations and it is shown that excitonic effects are very dominant due to the poor electronic screening in the two-dimensional layer. In particular, the A and B absorption peaks orig- inate from two bound excitons located at different posi- tions in the Brillouin zone and not from a split valence band originating from spin-orbit coupling and interlayer interactions as often stated in the literature [6]. This leads to a very different interpretation of the absorption spectra of MoS 2 and related dichalcogenides [12] and re- solves the puzzle of why the double exciton is preserved in single layer structures, which do not have a split va- lence band[13, 14]. The high luminescence yield in mono- layer MoS 2 can be attributed to the high binding en- ergy (0.7 eV ) of the A exciton, which strongly reduces the probability that excited electrons decay to the low- est point in the conduction band before recombining. In bilayer and bulk MoS 2 the difference between the direct and the indirect gap is larger and the exciton binding en- ergies are lower, thus enhancing the probability for non- radiative decay of the excitons. The many-body calculations described in this work were performed with the Yambo code[17] and the ini- tial Kohn-Sham electronic structure was obtained with the DFT code ABINIT [18] using the LDA exchange- correlation functional, a plane wave cutoff of 500 eV , and a 45 × 45 k-point grid centered at the Γ point. We have used the experimental lattice constants for MoS 2 and for the single layer calculations the repeated layers were separated by 23 ˚ A, whereas we used a separation of 29.3 ˚ A for the two layer calculations. For the one and two-layer calculations we used a Coulomb cutoff [19] in the direction perpendicular to the slabs to ensure con- vergence with respect to super cell size. The band struc- ture was obtained within the G 0 W 0 approximation [20] with a plane wave cutoff of 60 eV for the dielectric func- tion, which ensures convergence of the gap to within 60 meV[28]. Unless stated otherwise the full frequency de- pendence of the response function has been taken into account. While the use of a plasmon-pole approxima-