Michele Lazzeri

Raman Spectrum of Graphene and Graphene Layers

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 graphenes 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.

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Breakdown of the adiabatic Born-Oppenheimer approximation in graphene.

Engineering Department, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3 0FA,UK IMPMC, Universités Paris 6 et 7, CNRS, IPGP, 140 rue de Lourmel, 75015 Paris, France Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK The Born-Oppenheimer approximation (BO) [1] is the standard ansatz to describe the interaction between electrons and nuclei. BO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground-state. BO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond BO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur [2]. The use of BO to describe lattice motion in metals is, therefore, questionable [3, 4]. In spite of this, BO has proven effective for the accurate determination of chemical reactions [5], molecular dynamics [6, 7] and phonon frequencies [9, 8, 10] in a wide range of metallic systems. Graphene, recently discovered in the free state [11, 12], is a zero band-gap semiconductor [13], which becomes a metal if the Fermi energy is tuned applying a gate-voltage Vg [14, 12]. Graphene electrons near the Fermi energy have twodimensional massless dispersions, described by Dirac cones. Here

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.

Nonadiabatic Kohn anomaly in a doped graphene monolayer.

We compute, from first principles, the frequency of the E(2g), Gamma phonon (Raman G band) of graphene, as a function of the charge doping. Calculations are done using (i) the adiabatic Born-Oppenheimer approximation and (ii) time-dependent perturbation theory to explore dynamic effects beyond this approximation. The two approaches provide very different results. While the adiabatic phonon frequency weakly depends on the doping, the dynamic one rapidly varies because of a Kohn anomaly. The adiabatic approximation is considered valid in most materials. Here, we show that doped graphene is a spectacular example where this approximation miserably fails.

Phonon linewidths and electron-phonon coupling in graphite and nanotubes

We show 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 Glinewidths. The experimental EPCs compare extremely well with those from the 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 Gpeak in metallic nanotubes to a resonance between phonons and plasmons and we attribute it to a resonance between phonons and electron-hole pairs. For metallic tubes, we assign the G + and Gpeaks to TO circumferential

First principles calculation of vibrational Raman spectra in large systems: signature of small rings in crystalline SiO2

We present an approach for the efficient calculation of vibrational Raman intensities in periodic systems within density functional theory. The Raman intensities are computed from the second order derivative of the electronic density matrix with respect to a uniform electric field. In contrast to previous approaches, the computational effort required by our method for the evaluation of the intensities is negligible compared to that required for the calculation of vibrational frequencies. As a first application, we study the signature of 3- and 4-membered rings in the Raman spectra of several polymorphs of SiO2, including a zeolite (H-ZSM-18) having 102 atoms per unit cell.

Clar’s Theory, π-Electron Distribution, and Geometry of Graphene Nanoribbons

We show that Clars theory of the aromatic sextet is a simple and powerful tool to predict the stability, the pi-electron distribution, the geometry, and the electronic/magnetic structure of graphene nanoribbons with different hydrogen edge terminations. We use density functional theory to obtain the equilibrium atomic positions, simulated scanning tunneling microscopy (STM) images, edge energies, band gaps, and edge-induced strains of graphene ribbons that we analyze in terms of Clar formulas. On the basis of their Clar representation, we propose a classification scheme for graphene ribbons that groups configurations with similar bond length alternations, STM patterns, and Raman spectra. Our simulations show how STM images and Raman spectra can be used to identify the type of edge termination.

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, which 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 nonequilibrium optical phonon heating induced by electron transport. We predict an effective temperature for optical phonons of thousands Kelvin.

Thermal conductivity of graphene and graphite: collective excitations and mean free paths.

We characterize the thermal conductivity of graphite, monolayer graphene, graphane, fluorographane, and bilayer graphene, solving exactly the Boltzmann transport equation for phonons, with phonon-phonon collision rates obtained from density functional perturbation theory. For graphite, the results are found to be in excellent agreement with experiments; notably, the thermal conductivity is 1 order of magnitude larger than what found by solving the Boltzmann equation in the single mode approximation, commonly used to describe heat transport. For graphene, we point out that a meaningful value of intrinsic thermal conductivity at room temperature can be obtained only for sample sizes of the order of 1 mm, something not considered previously. This unusual requirement is because collective phonon excitations, and not single phonons, are the main heat carriers in these materials; these excitations are characterized by mean free paths of the order of hundreds of micrometers. As a result, even Fouriers law becomes questionable in typical sample sizes, because its statistical nature makes it applicable only in the thermodynamic limit to systems larger than a few mean free paths. Finally, we discuss the effects of isotopic disorder, strain, and chemical functionalization on thermal performance. Only chemical functionalization is found to play an important role, decreasing the conductivity by a factor of 2 in hydrogenated graphene, and by 1 order of magnitude in fluorogenated graphene.