Showing papers by "Francesco Mauri published in 2007"

Breakdown of the adiabatic Born-Oppenheimer approximation in graphene.

Abstract: The adiabatic Born-Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics. ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO 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 ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur. The use of ABO to describe lattice motion in metals is, therefore, questionable. In spite of this, ABO has proved effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state, is a zero-bandgap semiconductor that becomes a metal if the Fermi energy is tuned applying a gate voltage, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO.

Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials

Abstract: We present a scheme for the calculation of magnetic response parameters in insulators using ultrasoft pseudopotentials. It uses the gauge-including projector augmented wave method [C. J. Pickard and F. Mauri, Phys. Rev. B 63, 245101 (2001)] to obtain all-electron accuracy for both finite and infinitely periodic systems. We consider in detail the calculation of NMR chemical shieldings. The approach is successfully validated first for molecular systems by comparing calculated chemical shieldings for a range of molecules with quantum chemistry results and then in the solid state by comparing $^{17}\mathrm{O}$ NMR parameters calculated for silicates with experiment.

Optical phonons in carbon nanotubes: Kohn anomalies, Peierls distortions, and dynamic effects

Abstract: 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.

Phonon anharmonicities in graphite and graphene.

Abstract: We determine from first principles the finite-temperature properties-linewidths, line shifts, and lifetimes-of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E(2g) mode is found to decrease with temperature; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate infrared-active E(1u) mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A(1)' mode at K dominate over E(2g) at Gamma and couple strongly with acoustic phonons, highlighting how ballistic transport in carbon-based interconnects requires careful engineering of phonon decays and thermalization.

Electron-phonon coupling and electron self-energy in electron-doped graphene: calculation of angular resolved photoemission spectra

Abstract: We obtain analytical expressions for the electron self-energy and the electron-phonon coupling in electron-doped graphene using electron-phonon matrix elements extracted from density functional theory simulations. From the electron self-energies we calculate angle-resolved photoemission spectra (ARPES). We demonstrate that the measured kink at $\ensuremath{\approx}\ensuremath{-}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ from the Fermi level is actually composed of two features, one at $\ensuremath{\approx}\ensuremath{-}0.195\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ due to the twofold-degenerate ${E}_{2g}$ mode, and a second one at $\ensuremath{\approx}\ensuremath{-}0.16\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ due to the ${A}_{1}^{\ensuremath{'}}$ mode. The electron-phonon coupling extracted from the kink observed in ARPES experiments is roughly a factor of 5.5 larger than the calculated one. This disagreement can be only partially reconciled by the inclusion of resolution effects. Indeed, we show that a finite resolution increases the apparent electron-phonon coupling by underestimating the renormalization of the electron velocity at energies larger than the kink positions. The discrepancy between theory and experiments is thus reduced to a factor of $\ensuremath{\approx}2.5$. From the linewidth of the calculated ARPES we obtain the electron relaxation time. A comparison with available experimental data in graphene shows that the electron relaxation time detected in ARPES is almost two orders of magnitudes smaller than that measured by other experimental techniques.

Doping in Carbon Nanotubes Probed by Raman and Transport Measurements

Abstract: In situ Raman experiments together with transport measurements have been carried out on carbon nanotubes as a function of gate voltage. In metallic tubes, a large increase in the Raman frequency of the $G^-$ band, accompanied by a substantial decrease of its linewidth, is observed with electron or hole doping. In addition, we see an increase in the Raman frequency of the $G^+$ band in semiconducting tubes. These results are quantitatively explained using ab initio calculations that take into account effects beyond the adiabatic approximation. Our results imply that Raman spectroscopy can be used as an accurate measure of the doping of both metallic and semiconducting nanotubes.

Kohn anomalies and nonadiabaticity in doped carbon nanotubes

Abstract: The high-frequency Raman-active phonon modes of metallic single-walled carbon nanotubes (SWCNT) are thought to be characterized by Kohn anomalies (KAs) resulting from the combination of SWCNT intrinsic one-dimensional nature and a significant electron-phonon coupling (EPC). KAs are expected to be modified by the doping-induced tuning of the Fermi energy level ${ϵ}_{F}$, obtained through the intercalation of SWCNTs with alkali atoms or by the application of a gate potential. We present a density-functional theory (DFT) study of the phonon properties of a (9,9) metallic SWCNT as a function of electronic doping. For such study, we use, as in standard DFT calculations of vibrational properties, the Born-Oppenheimer (BO) approximation. We also develop an analytical model capable of reproducing and interpreting our DFT results. Both DFT calculations and this model predict, for increasing doping levels, a series of EPC-induced KAs in the vibrational mode parallel to the tube axis at the $\mathbf{\ensuremath{\Gamma}}$ point of the Brillouin zone, usually indicated in Raman spectroscopy as the ${G}^{\ensuremath{-}}$ peak. Such KAs would arise each time a new conduction band is populated. However, we show that they are an artifact of the BO approximation. The inclusion of nonadiabatic effects dramatically affects the results, predicting KAs at $\mathbf{\ensuremath{\Gamma}}$ only when ${ϵ}_{F}$ is close to a band crossing ${E}_{X}$. For each band crossing, a double KA occurs for ${ϵ}_{F}={E}_{X}\ifmmode\pm\else\textpm\fi{}\ensuremath{\hbar}\ensuremath{\omega}∕2$, where $\ensuremath{\hbar}\ensuremath{\omega}$ is the phonon energy. In particular, for a $1.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ metallic nanotube, we predict a KA to occur in the so-called ${G}^{\ensuremath{-}}$ peak at a doping level of about ${N}_{\mathrm{el}}∕C=\ifmmode\pm\else\textpm\fi{}0.0015$ atom $({ϵ}_{F}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ and, possibly, close to the saturation doping level $({N}_{\mathrm{el}}∕C\ensuremath{\sim}0.125)$, where an interlayer band crosses the ${\ensuremath{\pi}}^{*}$ nanotube bands. Furthermore, we predict that the Raman linewidth of the ${G}^{\ensuremath{-}}$ peak significantly decreases for $\ensuremath{\mid}{ϵ}_{F}\ensuremath{\mid}\ensuremath{\geqslant}\ensuremath{\hbar}\ensuremath{\omega}∕2$. Thus, our results provide a tool to determine experimentally the doping level from the value of the KA-induced frequency shift and from the linewidth of the ${G}^{\ensuremath{-}}$ peak. Finally, we predict KAs to occur in phonons with finite momentum $\mathbf{q}$ not only in proximity of a band crossing but also each time a new band is populated. Such KAs should be observable in the double-resonant Raman peaks, such as the defect-activated $D$ peak, and the second-order peaks $2D$ and $2G$.

Calcium Phosphates and Hydroxyapatite: Solid State NMR Experiments and First Principles Calculations

Abstract: Various calcium phosphates and hydroxyapatite (HAp) have been fully characterized by one- and two-dimensional solid-state nuclear magnetic resonance (NMR) experiments and first principles calculations of NMR parameters, such as chemical shift anisotropy (CSA) and electric field gradient tensors for all nuclei. Such compounds act as useful biocompatible materials. The projector augmented wave (PAW) and gauge including PAW methods allowed the complete assignment of spectra, including 1H magic-angle spinning (MAS) spectra for which ultimate resolution is not attained experimentally. 1H CSA tensors and orientation of the principal axes systems have been also discussed. 17O parameters have been calculated for a large variety of oxo-bridges and terminal oxygen atoms, including P–O–Si fragments characteristic for silicophosphate phases. The (δiso, CQ) sets of values allowed the clear distinction between the various oxygen atoms in a calculated 17O 3-quantum MAS experiment. Such an approach should be of great help for the description of interfaces in complex materials, in terms of structure and chemical composition.

Kohn anomalies and non-adiabaticity in doped carbon nanotubes

Abstract: The high-frequency Raman-active phonon modes of metallic single-walled carbon nanotubes (SWNTs) are thought to be characterized by Kohn anomalies (KAs), which are expected to be modified by the doping-induced tuning of the Fermi energy level $\epsilon_F$, obtained through the intercalation of SWNTs with alkali atoms or by the application of a gate potential. We present a Density-Functional Theory (DFT) study of the phonon properties of a (9,9) metallic SWNT as a function of electronic doping. For such study, we use, as in standard DFT calculations of vibrational properties, the Born-Oppenheimer (BO) approximation. We also develop an analytical model capable of reproducing and interpreting our DFT results. Both DFT calculations and this model predict, for increasing doping levels, a series of EPC-induced KAs in the vibrational mode parallel to the tube axis at the $\mathbf\Gamma$ point of the Brillouin zone, usually indicated in Raman spectroscopy as the $G^-$ peak. Such KAs would arise each time a new conduction band is populated. However, we show that they are an artifact of the BO approximation. The inclusion of non-adiabatic (NA) effects dramatically affects the results, predicting KAs at $\mathbf\Gamma$ only when $\epsilon_F$ is close to a band crossing $E_{X}$. For each band crossing a double KA occurs for $\epsilon_F=E_{X}\pm \hbar\omega/2$, where $\hbar\omega$ is the phonon energy. In particular, for a 1.2 $nm$ metallic nanotube, we predict a KA to occur in the so-called $G^-$ peak at a doping level of about $N_{el}/C=\pm 0.0015$ atom ($\epsilon_F\approx \pm 0.1 ~eV$). Furthermore, we predict that the Raman linewidth of the $G^-$ peak significantly decreases for $|\epsilon_F| \geq \hbar\omega/2$.

A first principles theory of nuclear magnetic resonance J-coupling in solid-state systems

Abstract: A method to calculate NMR J-coupling constants from first principles in extended systems is presented. It is based on density functional theory and is formulated within a planewave-pseudopotential framework. The all-electron properties are recovered using the projector augmented wave approach. The method is validated by comparison with existing quantum chemical calculations of solution-state systems and with experimental data. The approach has also been applied to the silicophosphate, Si5O(PO4)6, giving P31–Si29-couplings which are in excellent agreement with experiment.

Electronic structure of heavily doped graphene: The role of foreign atom states

Abstract: Using density functional theory calculations we investigate the electronic structure of graphene doped by deposition of foreign atoms We demonstrate that, as the charge transfer to the graphene layer increases, the band structure of the pristine graphene sheet is substantially affected This is particularly relevant when Ca atoms are deposed on graphene at $\mathrm{Ca}{\mathrm{C}}_{6}$ stoichiometry Similarly to what happens in superconducting graphite intercalated compounds, a Ca band occurs at the Fermi level Its hybridization with the C states generates a strong nonlinearity in one of the ${\ensuremath{\pi}}^{*}$ bands below the Fermi level, at energies comparable to the graphene ${E}_{2g}$ phonon frequency This strong nonlinearity, and not many-body effects as previously proposed, explains the large and anisotropic values of the apparent electron-phonon coupling measured in angular resolved photoemission

Oxygen K -edge XANES of germanates investigated using first-principles calculations

Abstract: O K-edge x-ray absorption near-edge structure (XANES) spectra of {alpha}-quartz-type and rutile-type GeO{sub 2} polymorphs and of K{sub 2}Ge{sub 8}O{sub 17} have been analyzed using first-principles plane-wave pseudopotential calculations. XANES spectra have been calculated using supercell including core-hole effects and good agreement with experiment has been obtained. In the the case of GeO{sub 2} polymorphs, local density of empty states has been performed and peaks in the experimental spectra can be assigned to transitions involving hybridization of the O p orbitals with the Ge s, Ge p, Ge sp, and Ge d orbitals. Furthermore, peak positions in the theoretical spectra appear to be correlated with changes in the Ge-O-Ge angle as well as indirectly with the Ge coordination geometry. Analysis of O K-edge XANES spectra for individual O sites in K{sub 2}Ge{sub 8}O{sub 17} shows that oxygens shared between two fivefold Ge atoms or one fourfold and one fivefold Ge atom exhibit subtle shifts to lower energy of the peaks, which have been previously observed in alkali germanate glasses at and above the germanate anomaly.

Spin and orbital magnetic response in metals: Susceptibility and NMR shifts

Abstract: A DFT-based method is presented which allows the computation of all-electron NMR shifts of metallic compounds with periodic boundary conditions. NMR shifts in metals measure two competing physical phenomena. Electrons interact with the applied magnetic field (i) as magnetic dipoles (or spins), resulting in the Knight shift, and (ii) as moving electric charges, resulting in the chemical (or orbital) shift. The latter is treated through an extension to metals of the gauge-invariant projector augmented wave developed for insulators. The former is modeled as the hyperfine interaction between the electronic spin polarization and the nuclear dipoles. NMR shifts are obtained with respect to the computed shieldings of reference compounds, yielding fully ab initio quantities which are directly comparable to experiment. The method is validated by comparing the magnetic susceptibility of interacting and noninteracting homogeneous gas with known analytical results, and by comparing the computed NMR shifts of simple metals with experiment.

First Principles Calculations of NMR Parameters in Biocompatible Materials Science: The Case Study of Calcium Phosphates, β- and γ-Ca(PO3)2. Combination with MAS-J Experiments

Abstract: First principles calculations of 31P NMR parameters allow full characterization of biocompatible Ca(PO3)2 phases. A “bridge” is established between NMR experimental data and calcium phosphate structures through the FPC-NMR approach (first principles calculations-NMR). We believe that this approach can be extended to a large panel of structures in the frame of biocompatible materials.

Optical phonons of graphene and nanotubes

Abstract: We review the optical phonon dispersions of graphene. In particular, we focus on the presence of two Kohn anomalies in the highest optical phonon branch at the $\bf \Gamma$ and $\bf K$ points of the Brillouin zone. We then show how graphene can be used as a model for the calculation of phonons in carbon nanotubes. Finally, we present the beyond Born-Oppenheimer corrections to their phonon dispersions. These are experimentally revealed in the Raman spectra of doped samples.

Anharmonic and non-adiabatic effects in MgB2: Implications for the isotope effect and interpretation of Raman spectra

Abstract: We review the published calculations of the anharmonic effects in MgB 2 and show that different results are mainly related to the various degrees of approximation involved in the calculations. When all the leading order terms in anharmonic perturbation theory are included the magnitude of anharmonic effects is marginal. This result is in good agreement with the phonon dispersion measured by inelastic X-ray scattering showing weak anharmonic phonon frequency shift. However, Raman spectra display a feature having E 2 g symmetry at ∼12 meV above the available X-ray phonon dispersion near Γ . Raman data can be explained if dynamical effects beyond the adiabatic Born–Oppenheimer approximation and electron lifetime effects are included in the phonon self-energy, without invoking anharmonicity. Finally, we discuss the implications of weak anharmonicity for the interpretation of the isotope effect and conclude that the isotope effect is the most important unresolved issue in the physics of MgB 2 .

Weak anharmonic effects in MgB2 : A comparative inelastic x-ray scattering and Raman study

Abstract: We study anharmonic effects in MgB2 by comparing inelastic x-ray and Raman scattering together with ab initio calculations. Using high-statistics and high-q-resolution measurements we show that the E2g-mode linewidth is independent of temperature along Gamma-A. We show, contrary to previous claims, that the Raman-peak energy decreases as a function of increasing temperature, a behavior inconsistent with all the anharmonic ab initio calculations of the E2g mode at Gamma available in the literature. These findings and the excellent agreement between the x-ray-measured and ab initio—calculated phonon spectra suggest that anharmonicity is not the main mechanism determining the temperature behavior of the Raman-peak energy. The Raman-E2g-peak position and linewidth can be explained by large dynamical effects in the phonon self-energy. In light of the present findings, the commonly accepted explanation of the reduced isotope effect in terms of anharmonic effects needs to be reconsidered.

Nitrogen Donor Aggregation in 4H-SiC: g-Tensor Calculations

Abstract: The microscopic origin of the Nx EPR-lines observed in heavily nitrogen doped 4H-SiC and 6H-SiC is discussed with the help of EPR parameters calculated from first principles. Based on the symmetry of the g-tensors we propose a model with distant NC donor pairs on inequivalent lattice sites which are coupled to S=1 centers but with nearly vanishing zero-field splittings, giving rise to an essentially S=1/2 like spectrum. The proposed aggregation in neutral donor pairs can contribute to the saturation of the free concentration observed in heavily nitrogen doped SiC.

Structure, reactivity and spectroscopic properties of minerals from lateritic soils: insights from ab initio calculations

Abstract: We review here some recent applications of ab initio calculations to the modelling of spectroscopic and energetic properties of minerals, which are key components of lateritic soils or govern their geochemical properties. Quantum mechanical ab initio calculations are based on density functional theory and den- sity functional perturbation theory. Among the minerals investigated, zircon is a typical resistant pri- mary mineral. Its resistance to weathering is at the origin of the peculiar geochemical behaviour of Zr, an element often used in mass balance calculations of continental weathering. Numerical modelling gives a unique picture of the origin of the chemical durability and radiation-induced amorphization of zircon. We also present several applications of ab initio calculations to the description of properties of secondary minerals, such as kaolinite-group minerals and gibbsite. Special attention is given to the cal- culation of infrared and Raman spectra. Surface properties and particle shape are major properties of finely-divided materials such as clay minerals. We show how theoretical modelling of infrared spectro- scopic data provides information on natural samples at both the microscopic (atomic structure) and macroscopic (particle shape) length-scale. The systematic comparison of experimental and theoretical data significantly improves our understanding of mineral transformations during soil formation and evolution in lateritic environments.

Probing the doping in metallic and semiconducting carbon nanotubes by Raman and transport measurements

Abstract: In-situ Raman experiments together with transport measurements have been carried out on carbon nanotubes as a function of gate voltage In metallic tubes, a large increase in the Raman frequency of the $G^-$ band, accompanied by a substantial decrease of its line-width, is observed with electron or hole doping In addition, we see an increase in Raman frequency of the $G^+$ band in semiconducting tubes These results are quantitatively explained using ab-initio calculations that take into account effects beyond the adiabatic approximation Our results imply that Raman spectroscopy can be used as an accurate measure of the doping of both metallic and semiconducting nanotubes

New Insight in Scandium-Mediated Growth Techniques: Sc-Related Defects in 4H-SiC and 6H-SiC

Abstract: Scandium can be used to influence the stoichiometry of SiC during growth of the hexagonal polytypes. Using PL-EPR and total energy calculations in the framework of density functional theory, scandium is predicted to be built in predominantly at the Si-sublattice in form of ScSi acceptors with acceptor levels at 0.55 eV (6H-SiC) and 0.48 eV (4H-SiC). In addition, new PL-EPR spectra are found with a large anisotropy in the g-tensor suggesting defect pairs as an origin.

First‐Principles Full‐Potential Calculations of the Fe K Pre‐Edge and Near‐Edge Structure in Carbonmonoxy‐Myoglobin

Abstract: The sensitivity of polarized Fe K‐edge XANES spectra to Fe‐C‐O geometry is investigated in carbonmonoxy‐myoglobin (MbCO) using first‐principles non “muffin‐tin” calculations. Structures issued from the Protein Data Bank (PDB) are optimized using Car‐Parrinello dynamics and compared to experiment through simulations of X‐ray absorption spectra. In order to understand the origin of the spectral features, trial structures are also considered. This paper shows that the combination of simulations of both pre‐edge and near‐edge regions allows a quantitative description of the iron environment in MbCO.

Breakdown of the adiabatic approximation in a doped graphene monolayer and in metallic carbon nanotubes

Abstract: We compute, from first-principles, the frequency of the phonons associated to the Raman G-bands in a graphene monolayer and in metallic nanotubes as a function of the charge doping. In both cases, the frequency displays an important measurable shift in the range of doping reached experimentally. As a consequence, Raman spectroscopy can be used as a direct probe of the doping of these systems. Calculations are done using (i) the adiabatic Bom-Oppenheimer approximation and (ii) time-dependent perturbation theory to explore dynamic effects beyond this approximation. The two approaches provide very different results. The frequency shift of the G-band in graphene and of the G- in metallic tubes represent remarkable failures of the adiabatic Bom-Oppenheimer approximation.

Temperature dependent phonon renormalization in metallic nanotubes

Abstract: We measure the temperature dependence of the Raman spectra of metallic and semiconducting nanotubes. We show that the different trend in metallic tubes is due to phonon re-normalization induced by the variation in electronic temperature, which is modeled including non-adiabatic contributions to account for the dynamic, time dependent nature