Vibrational and optical properties of MoS2: From monolayer to bulk

Abstract

Molybdenum disulfide, MoS 2 , has recently gained considerable attention as a layered material where neighboring layers are only weakly interacting and can easily slide against each other. Therefore, mechanical exfoliation allows the fabrication of single and multi-layers and opens the possibility to generate atomically thin crystals with outstanding properties. In contrast to graphene, it has an optical gap of 1.9 eV. This makes it a prominent candidate for transistor and opto-electronic applications. Single-layer MoS 2 exhibits remarkably different physical properties compared to bulk MoS 2 due to the absence of interlayer hybridization. For instance, while the band gap of bulk and multi-layer MoS 2 is indirect, it becomes direct with decreasing number of layers. In this review, we analyze from a theoretical point of view the electronic, optical, and vibrational properties of single-layer, few-layer and bulk MoS 2 . In particular, we focus on the effects of spinorbit interaction, number of layers, and applied tensile strain on the vibrational and optical properties. We examine the results obtained by different methodologies, mainly ab initio approaches. We also discuss which approximations are suitable for MoS 2 and layered materials. The effect of external strain on the band gap of single-layer MoS 2 and the crossover from indirect to direct band gap is investigated. We analyze the excitonic effects on the absorption spectra. The main features, such as the double peak at the absorption threshold and the high-energy exciton are presented. Furthermore, we report on the phonon dispersion relations of single-layer, few-layer and bulk MoS 2 . Based on the latter, we explain the behavior of the Raman-active A 1g and E 1 2g modes as a function of the number of layers. Finally, we compare theoretical and experimental results of Raman, photoluminescence, and optical-absorption spectroscopy.

Investigation of indirect excitons in bulk 2H-MoS2using transmission electron energy-loss spectroscopy

“…2 from the effective hole and electron masses at the respective high symmetry points. The used effective electron and hole masses are listed in Table III. (a) EMA fit parameters and results (b) Estimated effective exciton mass (in units of electron mass m0) with the estimated masses based on the electron and hole masses calculated by Molina-Sánchez et al 38 The K v1 -K ′ c exciton assumes an approximately linear dispersion. Based on theoretical considerations, Cudazzo et al 49 determined that in single-layer materials Wannier-like excitons exhibit a parabolic dispersion while Frenkel-like excitons show a linear momentum-dependence.…”

“…2. Molina-Sánchez et al performed G 0 W 0 calculations including spin orbit coupling (SOC) (and G 0 W 0 -SOC as well as self-consistent G 0 W 0 -SOC calculations with optimized bulk structure [optB86-vdW]) yielding an effective hole mass of 0.40 m 0 (and 0.39 m 0 as well as 0.40 m 0 ) and an effective electron mass of 0.58 m 0 for the same locations and directions as before 38. For those values, the estimated effective exciton mass was 0.98 m 0…”

Electronic Band Structure of Transition Metal Dichalcogenides from Ab Initio and Slater–Koster Tight-Binding Model

“…The electronic properties of these materials are highly sensitive to external conditions such as strain, pressure or temperature. For instance, a direct-to-indirect gap and even a semiconducting-to-metal transition can be induced under specific conditions [5][6][7][8][9][10]. They also present a strong spin-orbit coupling (SOC) that, due to the absence of inversion symmetry in single layer samples, lifts the spin degeneracy of the energy bands [11].…”

Ultrafast band-gap renormalization and build-up of optical gain in monolayer MoTe2

“…Furthermore, the conduction bands display a spin splitting of −35 meV and side valleys at the Σ/Λ points, that are 97 meV (Σ ↑ /Λ ↓ ) and 82 meV (Λ ↑ /Σ ↓ ) above the respective K/K -valley minima. These values are on the lower end of the range of published values that have been obtained using different functionals for the exchange correlation potential or GW corrections [32][33][34] and sufficiently large to prevent an excitation induced transition from a direct to indirect band gap 35,36 .…”