Ludger Wirtz

The phonon dispersion of graphite revisited

Abstract We review calculations and measurements of the phonon dispersion relation of graphite. First-principles calculations using density-functional theory are generally in good agreement with the experimental data since the long-range character of the dynamical matrix is properly taken into account. Calculations with a plane-wave basis demonstrate that for the in-plane optical modes, the generalized-gradient approximation (GGA) yields frequencies lower by 2% than the local-density approximation (LDA) and is thus in better agreement with experiment. The long-range character of the dynamical matrix limits the validity of force-constant approaches that take only interaction with few neighboring atoms into account. However, by fitting the force-constants to the ab initio dispersion relation, we show that the popular 4th-nearest-neighbor force-constant approach yields an excellent fit for the low frequency modes and a moderately good fit (with a maximum deviation of 6%) for the high-frequency modes. If, in addition, the non-diagonal force-constant for the second-nearest neighbor interaction is taken into account, all the qualitative features of the high-frequency dispersion can be reproduced and the maximum deviation reduces to 4%. We present the new parameters as a reliable basis for empirical model calculations of phonons in graphitic nanostructures, in particular carbon nanotubes.

Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS2

We present converged ab-initio calculations of the optical absorption spectra of single-layer, bi-layer, and bulk MoS

Raman imaging of doping domains in graphene on SiO2

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Tight-binding description of the quasiparticle dispersion of graphite and few-layer graphene

. Both the quasiparticle-energy calculations (on the level of the GW approximation) and the calculation of the absorption spectra (on the level of the Bethe-Salpeter equation) explicitly include spin-orbit coupling, using the full spinorial Kohn-Sham wave-functions as input. Without excitonic effects, the absorption spectra would have the form of a step-function, corresponding to the joint-density of states of a parabolic band-dispersion in 2D. This profile is deformed by a pronounced bound excitonic peak below the continuum onset. The peak is split by spin-orbit interaction in the case of single-layer and (mostly) by inter-layer interaction in the case of double-layer and bulk MoS

Coupling of excitons and defect states in boron-nitride nanostructures

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Ultrafast Electron-Phonon Decoupling in Graphite

. The resulting absorption spectra are thus very similar in the three cases but the interpretation of the spectra is different. Differences in the spectra can be seen around 3 eV where the spectra of single and double-layer are dominated by a strongly bound exciton.

Graphene on Metallic Substrates: Suppression of the Kohn Anomalies in the Phonon Dispersion

We present spatially resolved Raman images of the G and 2D lines of single-layer graphene flakes. The spatial fluctuations of G and 2D lines are correlated and are thus shown to be affiliated with local doping domains. We investigate the position of the 2D line—the most significant Raman peak to identify single-layer graphene—as a function of charging up to ∣n∣≈4×1012cm−2. Contrary to the G line which exhibits a strong and symmetric stiffening with respect to electron and hole doping, the 2D line shows a weak and slightly asymmetric stiffening for low doping. Additionally, the linewidth of the 2D line is, in contrast to the G line, doping independent making this quantity a reliable measure for identifying single-layer graphene.

Phonon and plasmon excitation in inelastic electron tunneling spectroscopy of graphite

A.G. acknowledges the Marie Curie Foundation COMTRANS from the European Union. A.R. and C.A. are supported in part by Spanish MEC Grant No. FIS2007-65702-C02-01 , Grupos Consolidados UPV/EHU of the Basque Country Government Grant No. IT-319-07 European Community e-I3 ETSF and SANES Grant No. NMP4- CT-2006-017310 projects. L.W. acknowledges support from the French national research agency Project PJC05_6741 . R.S. acknowledges MEXT Grants Nos. 20241023 and No. 16076201 .

Doped Graphene as Tunable Electron−Phonon Coupling Material

The signature of defects in the optical spectra of hexagonal boron nitride (BN) is investigated using many-body perturbation theory. A single BN-sheet serves as a model for different layered BN nanostructures and crystals. In the sheet we embed prototypical defects such as a substitutional impurity, isolated boron and nitrogen vacancies, and the divacancy. Transitions between the deep defect levels and extended states produce characteristic excitation bands that should be responsible for the emission band around 4 eV, observed in luminescence experiments. In addition, defect bound excitons occur that are consistently treated in our ab initio approach along with the “free” exciton. For defects in strong concentration, the coexistence of both bound and free excitons adds substructure to the main exciton peak and provides an explanation for the corresponding feature in cathodo- and photoluminescence spectra.

Unified Description of the Optical Phonon Modes in N-Layer MoTe2

We report the ultrafast dynamics of the 47.4 THz coherent phonons of graphite interacting with a photoinduced non-equilibrium electron-hole plasma. Unlike conventional materials, upon photoexcitation the phonon frequency of graphite upshifts, and within a few picoseconds relaxes to the stationary value. Our first-principles density functional calculations demonstrate that the phonon stiffening stems from the light-induced decoupling of the non-adiabatic electron-phonon interaction by creating the non-equilibrium electron-hole plasma. Time-resolved vibrational spectroscopy provides a window on the ultrafast non-equilibrium electron dynamics.