Theory of double-resonant Raman spectra in graphene: intensity and line shape of defect-induced and two-phonon bands

We calculate the double resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes, and two-phonons ones. Phonon and electronic dispersions reproduce calculations based on density functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kind of idealized defects. For an excitation energy of $\epsilon_L=2.4$ eV, the agreement with measurements is very good and calculations reproduce: the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the D, $D'$, 2D and $2D'$ lines; the line shapes; the presence of small intensity lines in the 1800, 2000 cm$^{-1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. According to the present findings, the intensity ratio between the $2D'$ and 2D lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and $D'$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal

Electron Transport and Hot Phonons in Carbon Nanotubes

We demonstrate the key role of phonon occupation in limiting the high-field ballistic transport in metallic carbon nanotubes. In particular, we provide a simple analytic formula for the electron transport scattering length, that we validate by accurate first principles calculations on (6,6) and (11,11) nanotubes. The comparison of our results with the scattering lengths fitted from experimental I-V curves indicates the presence of a non-equilibrium optical phonon heating induced by electron transport. We predict an effective temperature for optical phonons of thousands Kelvin.Comment: 4 pages, 1 figur

Kohn Anomalies and Electron-Phonon Interaction in Graphite

We demonstrate that graphite phonon dispersions have two Kohn anomalies at the Gamma-E_2g and K-A'1 modes. The anomalies are revealed by two sharp kinks. By an exact analytic derivation, we show that the slope of these kinks is proportional to the square of the electron-phonon coupling (EPC). Thus, we can directly measure the EPC from the experimental dispersions. The Gamma-E_2g and K-A'1 EPCs are particularly large, whilst they are negligible for all the other modes at Gamma and K.Comment: 4 pages, 2 figure

Total energy global optimizations using non orthogonal localized orbitals

An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical potential, determining the number of electrons. We show that the minimization of the functional with respect to overlapping localized orbitals can be performed so as to attain directly the ground state energy, without being trapped at local minima. The present approach overcomes the multiple minima problem present within the original formulation of orbital based $O(N)$ methods; it therefore makes it possible to perform $O(N)$ calculations for an arbitrary system, without including any information about the system bonding properties in the construction of the input wavefunctions. Furthermore, while retaining the same computational cost as the original approach, our formulation allows one to improve the variational estimate of the ground state energy, and the energy conservation during a molecular dynamics run. Several numerical examples for surfaces, bulk systems and clusters are presented and discussed.Comment: 24 pages, RevTex file, 5 figures available upon reques

Phonon Linewidths and Electron Phonon Coupling in Nanotubes

We prove that Electron-phonon coupling (EPC) is the major source of broadening for the Raman G and G- peaks in graphite and metallic nanotubes. This allows us to directly measure the optical-phonon EPCs from the G and G- linewidths. The experimental EPCs compare extremely well with those from density functional theory. We show that the EPC explains the difference in the Raman spectra of metallic and semiconducting nanotubes and their dependence on tube diameter. We dismiss the common assignment of the G- peak in metallic nanotubes to a Fano resonance between phonons and plasmons. We assign the G+ and G- peaks to TO (tangential) and LO (axial) modes.Comment: 5 pages, 4 figures (correction in label of fig 3

The Raman Fingerprint of Graphene

Graphene is the two-dimensional (2d) building block for carbon allotropes of every other dimensionality. It can be stacked into 3d graphite, rolled into 1d nanotubes, or wrapped into 0d fullerenes. Its recent discovery in free state has finally provided the possibility to study experimentally its electronic and phonon properties. Here we show that graphene's electronic structure is uniquely captured in its Raman spectrum that clearly evolves with increasing number of layers. Raman fingerprints for single-, bi- and few-layer graphene reflect changes in the electronic structure and electron-phonon interactions and allow unambiguous, high-throughput, non-destructive identification of graphene layers, which is critically lacking in this emerging research area

Pulsating Strings in Deformed Backgrounds

This is a brief summary on pulsating strings in beta deformed backgrounds found recently.Comment: 8 pages. Talk presented at Quantum Theory and Symmetries 7, Prague, August 7-13, 201

Phonon surface mapping of graphite: disentangling quasi--degenerate phonon dispersions

The two-dimensional mapping of the phonon dispersions around the $K$ point of graphite by inelastic x-ray scattering is provided. The present work resolves the longstanding issue related to the correct assignment of transverse and longitudinal phonon branches at $K$. We observe an almost degeneracy of the three TO, LA and LO derived phonon branches and a strong phonon trigonal warping. Correlation effects renormalize the Kohn anomaly of the TO mode, which exhibits a trigonal warping effect opposite to that of the electronic band structure. We determined the electron--phonon coupling constant to be 166$\rm(eV/\AA)^2$ in excellent agreement to $GW$ calculations. These results are fundamental for understanding angle-resolved photoemission, double--resonance Raman and transport measurements of graphene based systems