Ab initiostudy of the optical absorption and wave-vector-dependent dielectric response of graphite

Abstract

We performed ab initio calculations of the optical absorption spectrum and the wave-vector-dependent dielectric and energy-loss functions of graphite in the framework of the random-phase approximation. In the absorption spectrum, the most prominent peaks were analyzed in terms of interband transitions from specific regions of the Brillouin zone. The inclusion of the crystal local-field effects (LFE) in the response had an important influence on the absorption spectrum for light polarization parallel to the c axis. The calculated electron energy-loss spectra, even without LFE, were in very good agreement with existing momentumdependent energy-loss experiments concerning the peak positions of the two valence-electron plasmons. Important aspects of the line shape and anisotropy of the energy-loss function at large momentum transfer q were also well described: the splitting of the total ͑ + ͒ plasmon and the appearance of peaks originating from interband transitions. Finally, the role of the interlayer interaction was studied, in particular with regard to its effect on the absorption spectrum for light polarization parallel to c, and to the position of the higher-frequency + plasmon.

Ab initiostudy of the dielectric response of crystalline ropes of metallic single-walled carbon nanotubes: Tube-diameter and helicity effects

“…The diametrically opposed wall segments will interact more weakly at larger distances with increasing tube diameter, yielding a downward shift of the plasmon frequency. A similar effect was observed in our previous study 27 of the dielectric response in graphite and in graphene-sheet geometries of various intersheet distances: smaller intersheet distances lead to + -plasmon peaks at higher frequencies.…”

“…44 In agreement with experimental energy-loss data obtained from bulk single-walled nanotube material 10 we find hence the two valence plasmons to be consistently lower in energy than in graphite ͑see inset͒ where the plas- mon energies for small in-plane q are 7.2 and 28 eV, respectively. 27 The higher-energy + plasmon peak does not display a strong diameter dependence. For the ͑5,5͒ case it is slightly displaced to a lower frequency; this is consistent with the average electron density being smaller for this largerdiameter tube, therefore, lowering the plasmon frequency according to homogeneous electron-gas theory.…”

“…At higher frequencies, starting at 8 eV, the smallerdiameter tubes ͓especially the ͑3,3͒ ones͔ exhibit an absorption structure which is nonexistent in graphite 27 and which progressively diminishes in intensity with increasing tube diameter ͑see Fig. 5; also discussed in Fig.…”

“…Furthermore, our EELS calculations in graphite matched very well the experimentally observed spectra and plasmon-peak positions. 26,27 Here, we focus on the armchair series of carbon tubes, namely, of the type ͑n , n͒ with the index n ranging from 3 to 8, covering a diameter range up to roughly 11 Å. This allowed us to study systematically the induced changes in the dielectric functions with increasing tube diameter for these metallic tubes.…”

Many‐body effects in optical response of graphene‐based structures

“…[37] There, the energy-loss function is calculated from the dielectric response of the noninteracting electrons to external and induced fields. In Figure 4, a typical EEL spectrum measured for monolayer graphene [23] is superimposed with that calculated within the RPA.…”