Inhomogeneous optical absorption around the K point in graphite and carbon nanotubes

The optical absorption spectra of \ensuremath{\pi} electrons are calculated for graphite and carbon nanotubes. Particular attention is paid to the processes contributing to the optical absorption as a function of the electron wave vector k and light polarization direction. The optical absorption amplitude around the K point in the Brillouin zone has a node in the two-dimensional Brillouin zone of graphite. The formula for the absorption scattering matrix around the K point is given analytically by expanding the matrix element into a Taylor series. The chirality dependence of the absorption matrix element of a single-wall carbon nanotube is presented.

[1]  M. Dresselhaus,et al.  Competing spring constant versus double resonance effects on the properties of dispersive modes in isolated single-wall carbon nanotubes , 2003 .

[2]  R. Smalley,et al.  Structure-Assigned Optical Spectra of Single-Walled Carbon Nanotubes , 2002, Science.

[3]  Bennett B. Goldberg,et al.  Polarized resonant Raman study of isolated single-wall carbon nanotubes: Symmetry selection rules, dipolar and multipolar antenna effects , 2002 .

[4]  J. Hafner,et al.  Anomalous two-peak G'-band Raman effect in one isolated single-wall carbon nanotube , 2002 .

[5]  M. Dresselhaus,et al.  Probing phonon dispersion relations of graphite by double resonance Raman scattering. , 2001, Physical review letters.

[6]  J. Hafner,et al.  Electronic transition energy E ii for an isolated ( n , m ) single-wall carbon nanotube obtained by anti-Stokes/Stokes resonant Raman intensity ratio , 2001 .

[7]  J. M. Pitarke,et al.  Optical absorption and energy-loss spectra of aligned carbon nanotubes , 2001, cond-mat/0105443.

[8]  Charles M. Lieber,et al.  Structural ( n, m) determination of isolated single-wall carbon nanotubes by resonant Raman scattering. , 2001, Physical review letters.

[9]  Zhonghua Yu,et al.  Rayleigh and Raman Scattering from Individual Carbon Nanotube Bundles , 2001 .

[10]  M. Burghard,et al.  Polarized raman spectroscopy on isolated single-wall carbon nanotubes. , 2000, Physical review letters.

[11]  Thomsen,et al.  Double resonant raman scattering in graphite , 2000, Physical review letters.

[12]  W. H. Li,et al.  Spiral magnetic structure of Fe in Van der Waals gapped FeOCl and polyaniline-intercalated FeOCl , 2000 .

[13]  Rao,et al.  Rao et al. reply: , 2000, Physical review letters.

[14]  Cheng,et al.  Polarized raman study of single-wall semiconducting carbon nanotubes , 2000, Physical review letters.

[15]  M. Dresselhaus,et al.  Phonons in carbon nanotubes , 2000 .

[16]  C. Trautmann,et al.  Swelling effects in lithium fluoride induced by swift heavy ions , 2000 .

[17]  M. Damnjanović,et al.  Optical dichroism in nanotubes , 2000, cond-mat/0004365.

[18]  Rao,et al.  Polarized raman study of aligned multiwalled carbon nanotubes , 2000, Physical review letters.

[19]  Riichiro Saito,et al.  Trigonal warping effect of carbon nanotubes , 2000 .

[20]  Nobutsugu Minami,et al.  Amphoteric doping of single-wall carbon-nanotube thin films as probed by optical absorption spectroscopy , 1999 .

[21]  S. Louie,et al.  Disorder, Pseudospins, and Backscattering in Carbon Nanotubes , 1999, cond-mat/9906055.

[22]  Riichiro Saito,et al.  Berry's Phase and Absence of Back Scattering in Carbon Nanotubes. , 1998 .

[23]  A. M. Rao,et al.  Diameter-Selective Raman Scattering from Vibrational Modes in Carbon Nanotubes , 1997, Science.

[24]  Fujita,et al.  Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. , 1996, Physical review. B, Condensed matter.

[25]  T. Ando,et al.  Aharonov-Bohm effect in carbon nanotubes , 1994 .

[26]  Hiroshi Ajiki,et al.  Magnetic Properties of Carbon Nanotubes , 1993 .