The optical properties of transition metal dichalcogenide monolayers such as the two-dimensional semiconductors MoS2 and WSe2 are dominated by excitons, Coulomb bound electron-hole pairs. The light emission yield depends on whether the electron-hole transitions are optically allowed (bright) or forbidden (dark). By solving the Bethe Salpeter Equation on top of GW wave functions in density functional theory calculations, we determine the sign and amplitude of the splitting between bright and dark exciton states. We evaluate the influence of the spin-orbit coupling on the optical spectra and clearly demonstrate the strong impact of the intra-valley Coulomb exchange term on the dark-bright exciton fine structure splitting. PACS numbers:Introduction.-Transition metal dichalcogenide (TMDC) monolayers (MLs), with chemical formula MX 2 , with M=Mo or W and X=S, Se or Te, are semiconductors with a direct bandgap in the visible region situated at the K-point of the Brillouin zone [1,2]. In these 2D systems the broken inversion symmetry of the crystal lattice allows for optical control of the valley degree of freedom [3][4][5][6]. Combined with strong spin-orbit coupling (SOC) this leads to valley-spin locking [7], opening exciting avenues for original applications in optoelectronics and spintronics. Tightly bound excitons [8][9][10][11], with binding energies around 0.5 eV, originate from the direct term of the electron-hole (e-h) Coulomb interaction, enhanced by the strong 2D quantum confinement, the large effective masses, and the reduced dielectric screening in 2D systems. While the energy spectra of these excitons have been intensively studied by combining both experimental and theoretical technics in the last years [12][13][14][15][16][17], little is known about their fine structure.For optoelectronics based on TMDC MLs it is important to clarify if the lowest energy transition is optically bright or optically dark (i.e. spin forbidden) [18]. This bright-dark exciton fine structure splitting governs the optical properties also of 2D semiconductor nanostructures such as III-V and II-VI quantum wells [19][20][21][22][23] as well as CdSe nanocrystals [24]. In particular, the measured low photo-or electro-luminescence yield and its increase with the temperature in monolayer WSe 2 has been interpreted recently in terms of dark excitons lying at lower energy compared to the bright ones [25][26][27][28][29]. This will also affect the efficiency of recently demonstrated WSe 2 or WS 2 light emitting devices [30,31]. For fundamental physics experiments an optically dark ground state can be an advantage, as it allows to study exciton quantum fluids in Bose-Einstein exciton condensates [32]. It is thus crucial to determine both the amplitude and sign of this bright-dark exciton splitting in TMDC MLs.

MoTe 2 belongs to the semiconducting transition-metal dichalcogenide family with certain properties differing from the other well-studied members (Mo,W)(S,Se) 2. The optical band gap is in the near-infrared region, and both monolayers and bilayers may have a direct optical band gap. We first simulate the single-particle band structure of both monolayer and bilayer MoTe 2 with density-functional-theory-GW calculations. We find a direct (indirect) electronic band gap for the monolayer (bilayer). By solving in addition the Bethe-Salpeter equation, we find similar energies for the direct exciton transitions in monolayers and bilayers. We then study the optical properties by means of photoluminescence (PL) excitation, reflectivity, time-resolved PL, and power-dependent PL spectroscopy. With differential reflectivity, we find a similar oscillator strength for the optical transition observed in PL in both monolayers and bilayers suggesting a direct transition in both cases. We identify the same energy for the B-exciton state in the monolayer and the bilayer. Following circularly polarized excitation, we do not find any exciton polarization for a large range of excitation energies. At low temperatures (T = 10 K), we measure similar PL decay times on the order of 4 ps for both monolayer and bilayer excitons with a slightly longer one for the bilayer. Finally, we observe a reduction of the exciton-exciton annihilation contribution to the nonradiative recombination in bilayers.

The low-energy dielectric properties of CaC 6 -a representative graphite intercalated compound (GIC)-were investigated by ab initio time-dependent density functional theory calculations with full inclusion of local field effects. The calculations predict the existence of several kinds of plasmons in CaC 6 with energy below 10 eV. The mode with the largest energy is a conventional "πp" mode strongly dispersing in the hexagonal basal plane and almost nondispersing in the perpendicular direction. In the 2.3-3 eV energy range, we find a long-lived intraband plasmon with negative (positive) dispersion with momentum transfer in (perpendicular to) the basal plane. In the 0-1.5 eV energy range, a mode with linear soundlike dispersion along all three high-symmetry directions is observed. All the three modes present strong anisotropy originated from the band structure. The physical origin of these excitation modes is discussed in terms of intra-and interband transitions. The crucial role of local field effects in the propagation of the two lowest-energy modes at large momentum transfers and in the determination of its dispersion over extended momentum-transfer region is analyzed.

We present a theoretical study of electronic and optical properties of the layered ReX 2 compounds (X = S, Se) upon dimensional reduction. The effect on the band gap character due to interlayer coupling is studied by means of self-energy corrected GW method for optimized and experimental sets of structure's data. Induced changes on the optical properties as well as optical anisotropy are studied through optical spectra as obtained by solving the Bethe-Salpeter equation. At the G 0 W 0 level of theory, when decreasing the thickness of the ReS 2 sample from bulk to bilayer and to a freestanding monolayer the band gap reminds direct, despite a change of the band-gap nature, with values increasing from 1.6, 2.0 and 2.4 eV respectively. For ReSe 2 , the fundamental band gap changes from direct for bulk phase (1.38 eV) to indirect in bilayer (1.73 eV) and becomes again direct for a single layer (2.05 eV). We discuss these results in terms of the renormalization of the band structure. We produce the polarization angular dependent optical response to explore the optical anisotropy present in our results, as well as the fine structure of the lowest excitonic peaks present in absorption spectra.

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We studied low-energy plasmons in ultrathin films of silver in the thickness regimes where the surface states as well as quantum-well states must play significant roles. Realistic band structure was adopted for assessing the quantum-mechanical effect on the low-energy charge dynamics. In addition to the expected quasi-twodimensional plasmon mode, we find the modes that resemble an acoustic surface plasmon on semi-infinite metal surfaces and an additional plasmon mode related to the interband transitions between the two slab-split surface states. It is found that the dispersion of the latter mode is almost identical to the acoustic surface plasmon except the energy offset at small momenta values. The peaks in the surface response function related to interband transitions between the surfacelike states and bulklike states are identified as well. The present work elucidates the role of quantized electronic states and surface states on the plasmonic excitations in the ultimately thin films potentially used in the future nano-optics devices.

Collective electronic excitations associated with a potassium monolayer (1 ML) on a Be(0001) substrate are studied using ab initio evaluations of the surface response function with the use of energies and wave functions obtained from the selfconsistent pseudopotential calculations. The plasmon dispersion relations as well as real and imaginary parts of the dynamical induced charge density oscillations are presented. Comparison of the collective modes of the 1 ML K/Be(0001) system with that of a clean Be(0001) surface is given. It is shown that the K monolayer adsorption leads to appearance, additionally to the conventional surface plasmon of a clean Be surface, of a low-energy mode with characteristic acoustic-like dispersion in the 0-2 eV energy range. The existence of this mode owes to the presence of a K-induced quantum-well-state band whose wave function is strongly localized in the K adlayer. Also we observe a K-derived multipole plasmon with energy around 3 eV. Some other modifications in the Be surface plasmon properties upon K adsorption are discussed as well. 1 Introduction The study of electronic excitations in thin adsorbed alkali metal layers was an active topic for more than four decades . These systems are of interest because they show variety of phenomena such as work function changes, metal-insulator transitions, and surface reconstruction. In particular, they allow to investigate in great details the evolution of various basic physical properties of metal surfaces by changing the alkali adatom coverage. Thus the change in the screening properties (in particular, the strong non-locality of the screened interaction) at the surfaces in general [24]

We investigate within a two‐component jellium model the collective electronic excitations in a one‐monolayer (1ML) potassium covered beryllium surface. The calculations of the surface dynamical response properties have been performed with one‐particle energies and wave functions derived from the Kohn‐Sham density‐functional theory. The dispersion relation for the surface plasmon modes as well as the real and imaginary parts of the induced dynamical charge density oscillations are presented. Comparison of the collective modes in the 1ML K/Be system with that of a clean Be surface is made. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)