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We discover an excited bound three-particle state, the $2s$ trion, appearing energetically below the $2s$ exciton in monolayer ${\mathrm{WS}}_{2}$, using absorption spectroscopy and ab initio GW and Bethe-Salpeter equation calculations. The measured binding energy of the $2s$ trion (22 meV) is smaller compared to the $1s$ intravalley and intervalley trions (37 and 31 meV). With increasing temperature, the $1s$ and $2s$ trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted by $\sim 130$ meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions., main text, supplement

Interactions between atomic and molecular objects are to a large extent defined by the nanoscale electrostatic potentials which these objects produce. We introduce a scanning probe technique that enables three-dimensional imaging of local electrostatic potential fields with sub-nanometer resolution. Registering single electron charging events of a molecular quantum dot attached to the tip of a (qPlus tuning fork) atomic force microscope operated at 5 K, we quantitatively measure the quadrupole field of a single molecule and the dipole field of a single metal adatom, both adsorbed on a clean metal surface. Because of its high sensitivity, the technique can record electrostatic potentials at large distances from their sources, which above all will help to image complex samples with increased surface roughness., Comment: main text: 5 pages, 4 figures, supplementary information file: 4 pages, 2 figures

Charge-transfer (CT) excited states play an important role in the excited-state dynamics of DNA in aqueous solution. However, there is still much controversy on their energies. By ab initio many-body Green's function theory, together with classical molecular dynamics simulations, we confirm the existence of CT states at the lower energy side of the optical absorption maximum in aqueous DNA as observed in experiments. We find that the hydration shell can exert strong effects ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{eV}$) on both the electronic structure and CT states of DNA molecules through dipole electric fields. In this case, the solvent cannot be simply regarded as a macroscopic screening medium as usual. The influence of base stacking and base pairing on the CT states is also discussed.

Two state-of-the-art computational approaches: quantum Monte Carlo (QMC), based on accurate total energies, and GW with exciton effects (GW-BSE), based on perturbation theory are employed to calculate ionization potentials, electron affinities, and first excited singlet and triplet energies for the silane and methane molecules. Results are in excellent agreement between these dramatically different approaches and with available experiment. The optically forbidden triplet excitation in silane is predicted to lie roughly 1 eV higher than previously reported. For methane, the impact of geometry relaxation is shown to be $\sim$ 2 eV for excited states. Further, in the GW-BSE method, we demonstrate that inclusion of off-diagonal matrix elements in the self-energy operator is crucial for an accurate picture., Comment: Accepted to Physical Review Letters (11/15/00)

We study the two lowest-energy isomers of the Ge(111)-(2 x 1) surface, by a state-of-the-art first-principles calculation of their optical spectra, including the electron-hole interaction effects. A comparison of our results with the available experimental data suggests that, at difference with the silicon case, the stablest isomer differs from the standard "buckled Pandey chains" reconstruction. This conclusion is supported by accurate total-energy results.

We present an ab initio study of the optical properties of $\ensuremath{\alpha}$-quartz. The absorption spectrum is calculated by solving the Bethe-Salpeter equation for the interacting electron-hole system and found to be in excellent agreement with the measured spectrum up to 10 eV above the absorption threshold. We find that excitonic effects are crucial in understanding the sharp features in the absorption spectrum in this energy range. They are also crucial in the ab initio computation of the static dielectric constant, significantly enhancing its value.

The 6H-SiC(0001)-(sqrt[3]xsqrt[3])R30 degrees surface exhibits one half-filled localized dangling-bond orbital per surface unit cell. Its electronic structure can accurately be described as a Mott-Hubbard insulator. We investigate its spectrum by a spin-polarized ab initio quasiparticle calculation. The resulting band structure shows one occupied and one empty surface band, separated by a direct band gap of 1.95 eV. Since the band gap in the spectrum of the Hubbard model is directly given by the on-site Coulomb-interaction parameter U of the dangling-bond orbital, our results allow for a reliable determination of U = 1.95 eV.

We investigate excitons at the $\mathrm{Si}(111)\ensuremath{-}(2\ifmmode\times\else\texttimes\fi{}1)$ surface and their optical spectrum from first principles. This is done by solving the Bethe-Salpeter equation for the two-particle Green's function, including the electron-hole interaction. The optical spectrum of the surface is dominated by a surface exciton formed from the $\ensuremath{\pi}$-bonded surface states. The excitonic binding energy is more than 1 order of magnitude larger than in bulk Si. The two-particle wave function of the exciton state is strongly localized at the surface and exhibits distinct anisotropy due to the surface reconstruction.

We investigate optical absorption spectra and excitons in conjugated polymers from first principles. This is done by calculating the one-particle and the two-particle Green{close_quote}s function, including relevant many-body effects, and evaluating quasiparticle and optical excitations. Trans-polyacetylene and poly-phenylene-vinylene are studied as prototype long chain polymers. The electron-hole interaction gives rise to large exciton binding energies ({approximately}1 thinspthinspeV) and dramatically alters the optical spectra. The calculated exciton wave functions are very extended in real space. {copyright} {ital 1999} {ital The American Physical Society}

We present a new {ital abthinspthinspinitio} approach to calculate the interaction between electrons and holes in periodic crystals and to evaluate the resulting coupled electron-hole excitations. This involves a novel interpolation scheme in reciprocal space in solving the Bethe-Salpeter equation for the two-particle Green{close_quote}s function. We apply this approach to the calculation of the entire optical absorption spectrum, as well as of the energies and wave functions of bound exciton states in GaAs and LiF. Very good agreement with experiment is observed. {copyright} {ital 1998} {ital The American Physical Society}

We calculate the optical absorption spectrum of hydrogen-terminated silicon clusters by solving the Bethe-Salpeter equation for the two-particle Green{close_quote}s function using an {ital ab initio} approach. The one-particle Green{close_quote}s function and the electron-hole interaction kernel are calculated within the GW approximation for the electron self-energy operator. Very large exciton binding energies are observed. Our results for the one-particle properties and the optical absorption spectra of the clusters are in very good agreement with available experimental data. {copyright} {ital 1998} {ital The American Physical Society}

Recent experiments have indicated that dopants and defects can trigger new redshifted photoluminescence (PL) peaks below the ${E}_{11}$ peak in single-walled carbon nanotubes (SWCNTs). To understand the origin of the new PL peaks, we study theoretically the excited-state properties of SWCNTs with some typical dopants and defects by ab initio many-body perturbation theory. Our calculations demonstrate that the Stokes shift in doped centers can be as large as 170 meV, which is much larger than that of intact SWCNTs and must be taken into account. We find dipole-allowed transitions from localized midgap and shallow impurity levels, which can give rise to pronounced PL peaks. Dark excitons, on the other hand, seem to have oscillator strengths that are too small to account for the new PL peaks.

Optical excitations of molecular systems can be modified by their physical environment. We analyze the underlying mechanisms within many-body perturbation theory, which is particularly suited to study non-local polarizability effects on the electronic structure. Here we focus on the example of a semiconducting carbon nanotube, which observes redshifts of its excitons when the tube is touched by another nanotube or other physisorbates. We show that the redshifts mostly result from the polarizability of the attached ad-system. Electronic coupling may enhance the redshifts, but depends very sensitively on the structural details of the contact.

We discuss the adsorption of xenon and of PTCDA on the silver (111) surface within a first-principles approach, focusing on the adsorbate-substrate interaction energy as a function of distance. We combine exact exchange with correlation energy from the adiabatic-connection fluctuation-dissipation theorem. At a large distance Z from the surface, the correlation causes a van der Waals attraction [approximately -C3/(Z - Z0)3]. At a closer distance, the attraction deviates from its asymptotic form and, combined with the repulsive exact-exchange energy, yields an equilibrium in close agreement with experiment.

Normal incidence x-ray standing wave experiments and density functional theory reveal that 3,4,9,10-perylene-tetracarboxylic-dianhydride chemisorbs on Ag(111) in a nonplanar but vertically distorted configuration. The carboxylic O atoms are $0.18\ifmmode\pm\else\textpm\fi{}0.03\text{ }\AA{}$ closer to the surface than the perylene core. The distortion is related to weak, local bonds between carboxylic O atoms and the Ag surface which are coupled---through charge transfer into the former lowest unoccupied molecular orbital---to the primary, extended chemisorption bond via the perylene skeleton.

Carrier recombination at the Si(100) $c(4\ifmmode\times\else\texttimes\fi{}2)$ surface and the underlying surface electronic structure is unraveled by a combination of two-photon photoemission and many-body perturbation theory: An electron excited to the silicon conduction band by a femtosecond infrared laser pulse scatters within 220 ps to the unoccupied surface band, needs 1.5 ps to jump to the band bottom via emission of optical phonons, and finally relaxes within 5 ps with an excited hole in the occupied surface band to form an exciton living for nanoseconds.

We discuss electronic excitation processes at two ionic insulator surfaces, LiF(001)-(1 × 1) and MgO(001)-(1 X 1), within ab initio many-body perturbation theory. Because of the negative electron affinity of the surfaces,the lowest unoccupied electronic states are image states located in the vacuum outside the surface. Excitations of electrons from the surface layer into these image states are much lower in energy than the bulk excitons. They are responsible for characteristic surface features in the electron energy-loss spectra of LiF(001) and MgO(001).

Carrier recombination at the Si(100) c(4 x 2) surface and the underlying surface electronic structure is unraveled by a combination of two-photon photoemission and many-body perturbation theory: An electron excited to the silicon conduction band by a femtosecond infrared laser pulse scatters within 220 ps to the unoccupied surface band, needs 1.5 ps to jump to the band bottom via emission of optical phonons, and finally relaxes within 5 ps with an excited hole in the occupied surface band to form an exciton living for nanoseconds.

We investigate the initial decay of electron-hole excitations in a molecular layer after adsorption on an insulator substrate surface. This is done within ab initio many-body perturbation theory by calculating the time propagation of excited two-particle states. For a CO monolayer adsorbed on the MgO(001) surface we find very fast decay processes with lifetimes that are about 5 times shorter than the transfer of single charge carriers. This is due to a strong coupling of the molecular excitations to charge-transfer-exciton states between the adlayer and the substrate.

We discuss the localization of the surface exciton at the Si(111)- $(2\ifmmode\times\else\texttimes\fi{}1)$ surface due to self-trapping, which leads to a characteristic temperature-dependent linewidth of the optical response and to a significant Stokes shift of the luminescence. Self-trapping results in this case from a structural relaxation in the excited state, caused by the interplay between electronic and geometric degrees of freedom. The most significant contribution to this effect comes from one single geometric deformation mode which is driven by the internal electronic charge transfer in the self-trapped exciton.

Quasiparticle band structure calculations which include the most important cationic core states in the $\mathrm{GW}$ approximation of the self-energy operator are reported for a prototype II-VI semiconductor. The most salient feature of our results for cubic CdS is the finding that the complete cationic $N$ shell needs to be included in the pseudopotential and in the self-energy in order to obtain reasonable $\mathrm{GW}$ results in agreement with experiment.