By Dr. Ermin Malic, Prof. Dr. Andreas Knorr(auth.)
Chapter 1 creation – The Carbon Age (pages 1–8):
Chapter 2 Theoretical Framework (pages 9–50):
Chapter three Experimental ideas for the learn of Ultrafast Nonequilibrium provider Dynamics in Graphene (pages 51–82):
Chapter four leisure Dynamics in Graphene (pages 83–143):
Chapter five service Dynamics in Carbon Nanotubes (pages 145–163):
Chapter 6 Absorption Spectra of Carbon Nanotubes (pages 165–214):
Chapter 7 Absorption Spectrum of Graphene (pages 215–222):
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Extra info for Graphene and Carbon Nanotubes: Ultrafast Relaxation Dynamics and Optics
37) specifying in which direction the graphene sheet is wrapped into a cylinder, cp. 6. Because of the hexagonal symmetry of graphene, the chiral angle can take values between 0ı and 60ı . However, for each tube with 0ı Ä φ Ä 30ı an equivalent tube with 30ı Ä φ Ä 60ı can be found. Only the helix of graphene lattice points around the tube changes from right- to left-handed, which has an influence on optical selection rules [1, 84]. 6 Illustration of how a particular part of graphene can be rolled up into a specific carbon nanotube.
Two optical (LO, TO) and one acoustic (LA) modes are shown. Filled dots correspond to the measured data. Solid lines display the theoretical fit obtained from ab initio calculations. The shaded bars illustrate the approximately linear dispersion for acoustic and the approximately constant energy for optical phonons. Figure adapted from . 1 Optical Phonons The dispersion of optical phonons in graphene is characterized by two sharp kinks (Kohn anomalies) at the Γ and the K point , cp. 20.
63) i, j The conservation of momentum follows from the Kronecker deltas, which are obtained by evaluating the sums over the lattice vectors. 18 (a) Zoom-in of the Fourier transform of the Coulomb potential V AB (q z , Δ m) for the exemplary semiconducting (8, 4) nanotube as a function of the momentum transfer q z along the CNT axis. The figure illustrates the Coulomb contributions arising from processes with a momentum transfer perpendicular to the nanotube axis, that is, Δ m ¤ 0. (b) -30 -20 -10 0 -1 10 20 30 kz (nm ) The inset shows the most pronounced contribution with Δ m D 0.