Phonon renormalisation in doped bilayer graphene

We report phonon renormalisation in bilayer graphene as a function of doping. The Raman G peak stiffens and sharpens for both electron and hole doping, as a result of the non-adiabatic Kohn anomaly at the $\Gamma$ point. The bilayer has two conduction and valence subbands, with splitting dependent on the interlayer coupling. This results in a change of slope in the variation of G peak position with doping, which allows a direct measurement of the interlayer coupling strength.Comment: 5 figure

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

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

Optical Phonons in Carbon Nanotubes: Kohn Anomalies, Peierls Distortions and Dynamic Effects

We present a detailed study of the vibrational properties of Single Wall Carbon Nanotubes (SWNTs). The phonon dispersions of SWNTs are strongly shaped by the effects of electron-phonon coupling. We analyze the separate contributions of curvature and confinement. Confinement plays a major role in modifying SWNT phonons and is often more relevant than curvature. Due to their one-dimensional character, metallic tubes are expected to undergo Peierls distortions (PD) at T=0K. At finite temperature, PD are no longer present, but phonons with atomic displacements similar to those of the PD are affected by strong Kohn anomalies (KA). We investigate by Density Functional Theory (DFT) KA and PD in metallic SWNTs with diameters up to 3 nm, in the electronic temperature range from 4K to 3000 K. We then derive a set of simple formulas accounting for all the DFT results. Finally, we prove that the static approach, commonly used for the evaluation of phonon frequencies in solids, fails because of the SWNTs reduced dimensionality. The correct description of KA in metallic SWNTs can be obtained only by using a dynamical approach, beyond the adiabatic Born-Oppenheimer approximation, by taking into account non-adiabatic contributions. Dynamic effects induce significant changes in the occurrence and shape of Kohn anomalies. We show that the SWNT Raman G peak can only be interpreted considering the combined dynamic, curvature and confinement effects. We assign the G+ and G- peaks of metallic SWNTs to TO (circumferential) and LO (axial) modes, respectively, the opposite of semiconducting SWNTs.Comment: 24 pages, 21 figures, submitted to Phys. Rev.

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

Edge-functionalized and substitutional doped graphene nanoribbons: electronic and spin properties

Graphene nanoribbons are the counterpart of carbon nanotubes in graphene-based nanoelectronics. We investigate the electronic properties of chemically modified ribbons by means of density functional theory. We observe that chemical modifications of zigzag ribbons can break the spin degeneracy. This promotes the onset of a semiconducting-metal transition, or of an half-semiconducting state, with the two spin channels having a different bandgap, or of a spin-polarized half-semiconducting state -where the spins in the valence and conduction bands are oppositely polarized. Edge functionalization of armchair ribbons gives electronic states a few eV away from the Fermi level, and does not significantly affect their bandgap. N and B produce different effects, depending on the position of the substitutional site. In particular, edge substitutions at low density do not significantly alter the bandgap, while bulk substitution promotes the onset of semiconducting-metal transitions. Pyridine-like defects induce a semiconducting-metal transition.Comment: 12 pages, 5 figure

Raman Spectroscopy of Graphene Edges

Graphene edges are of particular interest since their orientation determines the electronic properties. Here we present a detailed Raman investigation of graphene flakes with edges oriented at different crystallographic directions. We also develop a real space theory for Raman scattering to analyze the general case of disordered edges. The position, width, and intensity of G and D peaks are studied as a function of the incident light polarization. The D-band is strongest for polarization parallel to the edge and minimum for perpendicular. Raman mapping shows that the D peak is localized in proximity of the edge. For ideal edges, the D peak is zero for zigzag orientation and large for armchair, allowing in principle the use of Raman spectroscopy as a sensitive tool for edge orientation. However, for real samples, the D to G ratio does not always show a significant dependence on edge orientation. Thus, even though edges can appear macroscopically smooth and oriented at well-defined angles, they are not necessarily microscopically ordered

Effect of Holstein phonons on the optical conductivity of gapped graphene

We study the optical conductivity of a doped graphene when a sublattice symmetry breaking is occurred in the presence of the electron-phonon interaction. Our study is based on the Kubo formula that is established upon the retarded self-energy. We report new features of both the real and imaginary parts of the quasiparticle self-energy in the presence of a gap opening. We find an analytical expression for the renormalized Fermi velocity of massive Dirac Fermions over broad ranges of electron densities, gap values and the electron-phonon coupling constants. Finally we conclude that the inclusion of the renormalized Fermi energy and the band gap effects are indeed crucial to get reasonable feature for the optical conductivity.Comment: 12 pages, 4 figures. To appear in Eur. Phys. J.