Christian Thomsen Vibrational properties of graphene and graphene nanoribbons Christian Thomsen Institut für Festkörperphysik TU Berlin

Christian Thomsen Topics Nanoribbon vibrations Graphene under uniaxial strain Graphene nanoribbons under uniaxial strain TERS: individual NTs and small bundles

Christian Thomsen Topics Nanoribbon vibrations Graphene under uniaxial strain Graphene nanoribbons under uniaxial strain TERS: individual NTs and small bundles

Christian Thomsen Graphite Graphene Nanoribbon strip of graphene „quasi 1D-crystal“ periodic in 1 direction 2D-crystal single graphite plane periodic in x-y-plane 3D-crystal sp2-hybridization stacked planes What are nanoribbons?

Christian Thomsen Potential for applications  high mobility  easy to prepare  band-gap engineering

Christian Thomsen Classification Zigzag Armchair width (number of dimers) ‏ edge type („chiral” NR not considered here) ‏ N-AGNRN-ZGNR

Christian Thomsen Wave propagation : continuous : quantized

Christian Thomsen Brillouin zone Brillouin zone of nanoribbons: N discrete lines (N: number of dimers) ‏ 6 modes for each line here: 10-AGNR and 10-ZGNR

Christian Thomsen Electronic properties: Armchair NRs => three families of AGNRs, N=3p, N=3p+1, N=3p+2 Son, Cohen, Louie PRL 97, (2006) ‏

Christian Thomsen Electronic properties: Zigzag NRs band gap opens for anti-ferromagnetic ground state metallic if spin is not considered Son, Cohen, Louie Nature 444, 347 (2006) ‏

Christian Thomsen Calculational details Siesta: Kohn-Sham self consistent density functional method norm-conserving pseudopotentials strictly confined atom centered numerical atomic orbitals (NAO) as basis functions phonon calculation: finite differences to obtain force constant matrix

Christian Thomsen Fundamental modes & “overtones” Interpretation as fundamental modes and overtones Nanoribbons have 3N modes E 2g corresponds to 0-LO and 0-TO A wavelength and a wavevector k perp can be assigned to overtones here: 7-AGNR ||

Christian Thomsen Width dependence (armchair) E2g

Christian Thomsen LO Softening (armchair) family dependence also in phonon spectrum strong softening of the LO phonon in 3p+2 ribbons

Christian Thomsen Mapping of the overtones graphene phonon dispersion: AGNR   KM ZGNR   M Mohr, CT et al., PRB 76, (2007) Mohr, CT et al., PRB 80, (2009) Grüneis, et al. PRB 65, (2002)

Christian Thomsen Mapping of the overtones Mapping of a 15-AGNR and a 8-ZGNR onto the graphene dispersion Mohr, CT et al., PRB 76, (2007) Mohr, CT et al., PRB 80, (2009) Grüneis, et al. PRB 65, (2002)

Christian Thomsen Graphite dispersion Double resonance: Grüneis, et al., PRB 65, (2002) Reich and CT, Phil. Trans. 362, 2271 (2004) Inelastic x-ray scattering: Maultzsch, CT, et al., PRL 92, (2004) Mohr, CT et al., PRB 76, (2007) unfolding nanoribbons: Gillen, CT et al., PRB 80, (2009) Gillen et al., PRB in print (2010)

Christian Thomsen Phonon dispersion Odd N: modes pairwise degenerate at X-point (zone-folding) 4 th acoustic mode („1-ZA“) (rotational mode) Even N: modes pairwise degenerate at X-point 4 th acoustic mode („1-ZA“) compare: Yamada et al, PRB, 77, (2008))

Christian Thomsen Topics Nanoribbon vibrations Graphene under uniaxial strain Graphene nanoribbons under uniaxial strain TERS: individual NTs and small bundles

Christian Thomsen Mohiuddin, Ferrari et al,. PRB 79, (2009) ‏ Huang, Heinz et al., PNAS 106, 7304 (2009) ‏ Uniaxial strain in graphene Polarized measurements reveal orientation of graphene sample

Christian Thomsen Calculational details Kohn-Sham selfconsistent density functional method norm-conserving pseudopotentials plane-wave basis phonon calculation: linear response theory / DFBT(Density Functional Perturbation Theory)‏

Christian Thomsen Method

Christian Thomsen Electronic band structure under strain

Christian Thomsen Dirac cone at K-point strains shift the Dirac cone but don’t open a gap

Christian Thomsen Phonon band structure under strain

Christian Thomsen Raman spectrum of graphene

Christian Thomsen Shift of the E 2g -mode shift rate independent of strain direction

Christian Thomsen Shift of the E 2g -mode

Christian Thomsen Ni et al., ACS Nano 2, 2301 (2008) Mohiuddin, Ferrari et al. PRB 79, (2009) Huang, Heinz et al., PNAS 106, 7304 (2009) Comparison with experiments excellent agreement with Mohiuddin/Ferrari Mohr, CT, et al., Phys. Rev. B 80, (2009)

Christian Thomsen D and 2D mode: Double resonance The particular band structure of CNTs allows an incoming resonance at any energy. The phonon scatters the electron resonantly to the other band. A defect scatters the electron elastically back to where it can recombine with the hole. q phonon varies strongly with incident photon energy. CT and Reich, Phys. Rev. Lett. 85, 5214 (2000)

Christian Thomsen Double resonance: inner and outer defect- induced D-mode

Christian Thomsen Strained w/ diff. polarizations

Christian Thomsen Topics Nanoribbon vibrations Graphene under uniaxial strain Graphene nanoribbons under uniaxial strain TERS: individual NTs and small bundles

Christian Thomsen NR-Band gap under strain  band gap for N=13, 14, 15 AGNRs  linear dependence for small strains

Christian Thomsen G + and G - modes as fct. of strain N=7

Christian Thomsen G - for different NR widths  approaching the dependence of graphene

Christian Thomsen  approaching the dependence of graphene G + for different NR widths

Christian Thomsen Topics Nanoribbon vibrations Graphene under uniaxial strain Graphene nanoribbons under uniaxial strain TERS: individual NTs and small bundles

Christian Thomsen Tip-enhanced Raman spectra  find specific nanotubes, previously identified with AFM  observe the RBM as a function of position along the nanotube  study frequency shifts as a function of sample- tip distance Hartschuh et al., PRL (2003) and Pettinger et al., PRL (2004) N.Peica, CT, J. Maultzsch, JRS, submitted (2010) N. Peica, CT et al., pss (2009)

Christian Thomsen TERS setup Laser wavelength 532 nm

Christian Thomsen Tip-enhanced Raman spectra small bundles of individual nanotubes on a silicon wafer

Christian Thomsen Tip-enhanced Raman spectra small bundles of individual nanotubes on a silicon wafer

Christian Thomsen Chirality: Raman spectra The Raman spectrum is divided into radial breathing mode defect-induced mode high-energy mode

Christian Thomsen Tip-enhanced Raman spectra small bundles of individual nanotubes on a silicon wafer N.Peica, CT, J. Maultzsch, Carbon, submitted (2010)

Christian Thomsen Sample-tip distance dependence enhancement factors between and

Christian Thomsen RBM spectra  RBM can be observed even if not visible in the far-field spectrum  identified (17,6), (12,8), (16,0), and (12,5) semiconducting NTs from experimental Kataura plots Popov et al. PRB 72, (2005)

Christian Thomsen Frequency shifts in TERS shifts of 5 cm -1 observed

Christian Thomsen Frequency shifts in TERS  possible explanation of the small shifts are in terms of the double-resonance Raman process of the D and 2D modes (CT, PRL 2000) deformation through the tip approach sensitive reaction of the electronic band structure

Christian Thomsen Conclusions Vibrations of graphene nanoribbons mapping of overtones on graphene (graphite) dispersion Uniaxial strain in graphene comparison to experiments TERS specta of individual NTs large enhancement factors NTs identified possible observation of small frequency shifts

Christian Thomsen Acknowledgments Janina Maultzsch Technische Universität Berlin Nils Rosenkranz Technische Universität Berlin Marcel Mohr Technische Universität Berlin Niculina Peica Technische Universität Berlin