By Dr. Ermin Malic, Prof. Dr. Andreas Knorr(auth.)
Chapter 1 advent – The Carbon Age (pages 1–8):
Chapter 2 Theoretical Framework (pages 9–50):
Chapter three Experimental thoughts for the examine of Ultrafast Nonequilibrium provider Dynamics in Graphene (pages 51–82):
Chapter four rest Dynamics in Graphene (pages 83–143):
Chapter five provider 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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Additional info for Graphene and Carbon Nanotubes: Ultrafast Relaxation Dynamics and Optics
Group-theoretical considerations yield K D (k z , m) D (2π/(3a), nr mod q). In the case of the best-known tubes of this type, the armchair nanotubes, this gives K D (2π/(3a), n), cp. 6. 10 Band structure of the exemplary (8, 4) carbon nanotube calculated with (a) linear quantum numbers (k z , m) and (b) helical quantum numbers ( kQz , m). Q The linear subband corresponding to the energetically lowest transition E11 is gray within the helical band structure. 1 Helical Quantum Numbers According to the Noether theorem, any symmetry corresponds to a conservation law for a related physical quantity, for example conservation of momentum results from the homogeneity of space.
This reflects the behavior of the matrix element for different linear subbands at the Γ point of zigzag nanotubes, that is, k z D 0, cp. 12a. It illustrates that M zvc (k z ) vanishes at the Γ point of graphene, that is for the linear subband m D 0 in zigzag CNTs. As already mentioned earlier, at this high-symmetry point, the optical absorption is forbidden in graphene. This selection rule carries over to nanotubes. 15 The square of the z-component of the optical matrix element Mzvc (k z ) along the high-symmetry line Γ K M in the Brillouin zone, cp.
In this region, the overlap s 0 can be neglected resulting in a simple expression for the dispersion relation in graphene ε˙ k D ˙γ0 je(k)j . 32) The nearest-neighbor contributions in e(k) can be further analytically evaluated by calculating the scalar product of the momentum k and the connecting vectors b i in Eq. 30) (cp. 3a) resulting in 1 a 2 )) C 2 cos (k a 2 ) C 2 cos (k a 1 ) 2 #1/2 ! p 3a 0 a0 Á D 3 C 2 cos(a 0 k y ) C 4 cos . 5 illustrates the band structure of graphene along the first hexagonal Brillouin zone.
Graphene and Carbon Nanotubes: Ultrafast Relaxation Dynamics and Optics by Dr. Ermin Malic, Prof. Dr. Andreas Knorr(auth.)