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The calculation of the electron–phonon coupling from first principles is computationally very challenging and remains mostly out of reach for systems with a large number of atoms. Semi-empirical methods, like density functional tight binding (DFTB), provide a framework for obtaining quantitative results at moderate computational costs. Herein, we present a new method based on the DFTB approach for computing electron–phonon couplings and relaxation times. It interfaces with PHONOPY for vibrational modes and DFTB+ to calculate transport properties. We derive the electron–phonon coupling within a non-orthogonal tight-binding framework and apply them to graphene as a test case.

We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

The thesis presents experimental studies of device characteristics and vibrational properties of atomic layer thin graphene and molybdenum disulphide (MoS2). We carried out Raman spectroscopic studies on field effect transistors (FET) fabricated from these materials to investigate the phonons renormalized by carrier doping thus giving quantitative information on electron-phonon coupling. Below, we furnish a synoptic presentation of our work on these systems. Chapter1: Introduction Chapter1, presents a detailed introduction of the systems studied in this the¬sis, namely single layer graphene (SLG), bilayer graphene (BLG) and single layer molybdenum disulphide (MoS2). We have mainly discussed their electronic and vibrational properties in the light of Raman spectroscopy. A review of the Raman studies on graphene layers is presented. Chapter2: Methodology and Experimental Techniques Chapter 2 starts with a description of Raman instrumentation. The steps for isolating graphene and MoS 2 flakes and the subsequent device fabrication procedures involving lithography are discussed in detail. A brief account of the top gated field effect transistor (FET) using solid polymer electrolyte is presented. Chapter3: Band gap opening in bilayer graphene and formation of p-n junction in top gated graphene transistors: Transport and Raman studies In Chapter3 the bilayer graphene (BLG) field effect transistor is fabricated in a dual gate configuration which enables us to control the energy band gap and the Fermi level independently. The gap in bilayer energy spectrum is observed through different values of the resistance maximum in the back gate sweep curves, each taken at a fixed top gate voltage. The gate capacitance of the polymer electrolyte is estimated from the experimental data to be 1.5μF/cm2 . The energy gap opened between the valence and conduction bands using this dual-gated geometry is es¬timated invoking a simple model which takes into account the screening of gate induced charges between the two layers. The presence of the controlled gap in the energy band structure along with the p-n junction creates a new possibility for the bilayer to be used as possible source of terahertz source. The formation of p-n junction along a bilayer graphene (BLG) channel is achieved in a electrolytically top gated BLG FET, where the drain-source voltage VDS across the channel is continuously varied at a fixed top gate voltage VT(VT>0). Three cases may arise as VDS is varied keeping VT fixed: (i) for VT-VDS0, the entire channel is doped with electron, (ii) for VT-VDS= 0, the drain end becomes depleted of carriers and kink in the IDS vs VDS curve appears, (iii) for VT-VDS « 0, carrier reversal takes place at the drain end, accumulation of holes starts taking place at the drain end while the source side is still doped with electrton. The verification of the spatial variation of carrier concentration in a similar top gated single layer graphene (SLG) FET device is done using spatially resolved Ra¬man spectroscopy. The signature 2D Raman band in a single layer graphene shows opposite trend when doped: 2D peak position decreases for electron doping while it increases for hole doping. On the other hand, the G mode response being symmetric in doping can act as a read-out for the carrier concentration. We monitor the peak position of the G and the 2D bands at different locations along the SLG FET channel. For a fixed top gate voltage V T , both G and the 2D band frequencies vary along the channel. For a positive VTsuch that VT-VDS= 0, the peak frequencies ωGand ω2DωG/2D occur at the undoped frequency (ωG/2D)n=0 near the drain end while the source end corresponds to non-zero concentration. When VT-VDS<0, Raman spectra from hole doped regions (drain end) in the channels show an blue-shift in ω2Dwhile from the electron doped regions (near source) ω2Dis softened. Chapter4: Mixing Of Mode Symmetries In Top Gated Bilayer And Multilayer Graphene Field Effect Devices In Chapter4, the effect of gating on a bilayer graphene is captured by using Raman spectroscopy which shows a mixing of different optical modes belonging to differ¬ent symmetries. The zone-center G phonon mode splits into a low frequency (Glow) and a high frequency (Ghigh) mode and the two modes show different dependence on doping. The two G bands show different trends with doping, implying different electron-phonon coupling. The frequency separation between the two sub-bands in¬creases with increased doping. The mode with higher frequency, termed as Ghigh, shows stiffening as we increase the doping whereas the other mode, Glow, shows softening for low electron doping and then hardening at higher doping. The mode splitting is explained in terms of mixing of zone-center in-plane optical phonons rep¬resenting in-phase and out-of-phase inter-layer atomic motions. The experimental results are combined with the theoretical predictions made using density functional theory by Gava et al.[PRB 80, 155422 (2009)]. Similar G band splitting is observed in the Raman spectra from multilayer graphene showing influence of stacking on the symmetry properties. Chapter5: Anomalous dispersion of D and 2D modes in graphene and doping dependence of 2D ′and 2D+G bands Chapter 5 consists of two parts: Part A titled “Doping dependent anomalous dispersion of D and 2D modes in graphene” describes the tunability of electron-phonon coupling (EPC) associated with the highest optical phonon branch (K-A) around the zone corner K using a top gated single layer graphene field effect transistor. Raman D and 2D modes originate from this branch and are dispersive with laser excitation energy. Since the EPC is proportional to the slope of the phonon branch, doping dependence of the D and 2D modes is carried out for different laser energies. The dispersion of the D mode decreases for both the electron and the hole doping, in agreement with the recent theory of Attaccalite et. al [Nano Letters, 10, 1172 (2010)]. In order to observe D-band in the SLG samples, low energy argon ion bombardment was carried out. The D peak positions for variable carrier concentration using top-gated FET geometry are determined for three laser energies, 1.96 eV, 2.41 eV and 2.54 eV. However, the dispersion of the 2D band as a function of doping shows an opposite trend. This most curious result is quantitatively explained us¬ing a fifth order process rather than the usual fourth order double resonant process usually considered for both the D and 2D modes. Part B titled “Raman spectral features of second order 2D’ and 2D+G modes in doped graphene transistor” deals with doping dependence of 2D’ and 2D+G bands in single layer graphene transistor. The phonon frequency blue shifts for the hole doping and whereas it red shifts for electron doping, similar to the behaviour of the 2D band. The linewidth of the 2D+G combination mode too follows the 2D trend increasing with doping while that of 2D’ mode remains invariant. Chapter6: New Raman modes in graphene layers using 2eV light Unique resonant Raman modes are identified at 1530 cm−1 and 1445 cm−1 in single, bi, tri and few layers graphene samples using 1.96 eV (633 nm) laser excitation energy (EL). These modes are absent in Raman spectra using 2.41 eV excitation energy. In addition, the defect-induced D band which is observed only from the edges of a pristine graphene sample, is observed from the entire sample region using E L = 1.96 eV. Raman images with peak frequencies centered at 1530 cm−1, 1445 cm−1 and D band are recorded to show their correlations. With 1.96 eV, we also observe a very clear splitting of the D mode with a separation of ∼32 cm−1, recently predicted in the context of armchair graphene nanoribbons due to trigonal warping effect for phonon dispersion. All these findings suggest a resonance condition at ∼2eVdue to homo-lumo gap of a defect in graphene energy band structure. Chapter7: Single and few layer MoS2: Resonant Raman and Phonon Renormalization Chapter 7 is divided into two parts. In Part A “Layer dependent Resonant Raman scattering of a few layer MoS2”, we discuss resonant Raman scattering from single, bi, four and seven layers MoS2. As bulk crystal of MoS2is thinned down to a few atomic layers, the indirect gap widens turning into a direct gap semiconductor with a band gap of 1.96 eV in its monolayer form. We perform Raman study from MoS 2 layers employing 1.96 eV laser excitation in order to achieve resonance condition. The prominent Raman modes for MoS 2 include first order E12g mode at ∼383 cm−1 and the A1gmode at ∼408 cm−1 which are observed under both non resonant and resonant conditions. A1gphonon involves the sulphur atomic vibration in opposite direction along the c axis (perpendicular to the basal plane) whereas for E12g mode, displacement of Mo and sulphur atoms are in the basal plane. With decreasing layer thickness, these two modes shifts in opposite direction, the E12g mode shows a blue shift of ∼2cm−1 while the A1gis red shifted by ∼4cm−1 . Under resonant condi¬tion, apart from E12g and A1gmodes, several new Raman spectral features, which are completely absent in bulk, are observed in single, bi and few layer spectra pointing out the importance of Raman characterization. New Raman mode attributed to the longitudinal acoustic mode belonging to the phonon branch at M along the Γ-M direction of the Brillouin zone is seen at ∼230 cm−1 for bi, four and seven layers. The most intense region of the spectrum around 460 cm−1 is characterized by layer dependent frequencies and spectral intensities with the band near 460 cm−1 becoming asymmetric as the sample thickness is increased. In the high frequency region between 510-630 cm−1, new bands are seen for bi, four and seven layers. In Part B titled “Symmetry-dependent phonon renormalization in monolayer MoS2transistor”, we show that in monolayer MoS2the two Raman-active phonons, A1g and E21 g, behave very differently as a function of doping induced by the top gate voltage in FET geometry. The FET achieves an on-off ratio of ∼ 105 for electron doping. We show that while E12g phonon is essentially unaffected, the A1gphonon is strongly influenced by the level of doping. We quantitatively understand our experimental results through the use of first-principles calculations to determine frequencies and electron-phonon coupling for both the phonons as a function of carrier concentration. We present symmetry arguments to explain why only A1g mode is renormalized significantly by doping. Our results bring out a quantitative under¬standing of electron-phonon interaction in single layer MoS2.

In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U-J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated self-consistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system's response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the two-field theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential U, coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries.

Cette thèse traite de la structure électronique de supraconducteurs telle que déterminée par la théorie de la fonctionnelle de la densité. Une brève explication de cette théorie est faite dans l’introduction. Le modèle de Hubbard est présenté pour pallier à des problèmes de cette théorie face à certains matériaux, dont les cuprates. L’union de deux théories donne la DFT+U, une méthode permettant de bien représenter certains systèmes ayant des électrons fortement corrélés. Par la suite, un article traitant du couplage électron- phonon dans le supraconducteur NbC1−xNx est présenté. Les résultats illustrent bien le rôle de la surface de Fermi dans le mécanisme d’appariement électronique menant à la supraconductivité. Grâce à ces résultats, un modèle est développé qui permet d’expliquer comment la température de transition critique est influencée par le changement des fré- quences de vibration du cristal. Ensuite, des résultats de calcul d’oscillations quantiques obtenus par une analyse approfondie de surfaces de Fermi, permettant une comparaison directe avec des données expérimentales, sont présentés dans deux articles. Le premier traite d’un matériau dans la famille des pnictures de fer, le LaFe2P2. L’absence de su- praconductivité dans ce matériau s’explique par la différence entre sa surface de Fermi obtenue et celle du supraconducteur BaFe2As2. Le second article traite du matériau à fermions lourds, le YbCoIn5. Pour ce faire, une nouvelle méthode efficace de calcul des fréquences de Haas-van Alphen est développée. Finalement, un dernier article traitant du cuprate supraconducteur à haute température critique YBa2Cu3O6.5 est présenté. À l’aide de la DFT+U, le rôle de plusieurs ordres magnétiques sur la surface de Fermi est étudié. Ces résultats permettent de mieux comprendre les mesures d’oscillations quan- tiques mesurées dans ce matériau. / In this thesis, the electronic structure of different kinds of superconductors is explored with the density functional theory. A brief explanation of this theory is done in the in- troduction. The Hubbard model is also presented as it can be used to solve shortcomings of the theory in some materials such as cuprates. The blend of the two theories is the DFT+U which is used to describe materials with strongly correlated electrons. After- ward, a paper describing the electron-phonon coupling in the superconductor NbC1−xNx is presented. Results from this work show the role of the Fermi surface in the electron pairing mechanism leading to superconductivity. Based on these results, a model is de- veloped explaining how the critical temperature is influenced by the change in frequency of the vibration modes. Then, quantum oscillation results based on a detailed analysis of Fermi surfaces, allowing a direct comparison with experimental data, are presented within two papers. The first one is about a material in the iron pnictide family, the LaFe2P2. Our calculations show that the Fermi surface of this material is different from the superconducting doped BaFe2As2 which explains why this material shows no sign of superconductivity. The second paper is about the heavy fermion system YbCoIn5. To do this, a new efficient method to calculate de Haas-van Alphen frequencies is developed. Finally, a paper on superconducting YBa2Cu3O6.5 is presented. Using DFT+U, the role of various magnetic orders on the Fermi surface are studied. The results allow a better understanding of the measured quantum oscillations in this material.

Cette thèse traite de la structure électronique de supraconducteurs telle que déterminée par la théorie de la fonctionnelle de la densité. Une brève explication de cette théorie est faite dans l’introduction. Le modèle de Hubbard est présenté pour pallier à des problèmes de cette théorie face à certains matériaux, dont les cuprates. L’union de deux théories donne la DFT+U, une méthode permettant de bien représenter certains systèmes ayant des électrons fortement corrélés. Par la suite, un article traitant du couplage électron- phonon dans le supraconducteur NbC1−xNx est présenté. Les résultats illustrent bien le rôle de la surface de Fermi dans le mécanisme d’appariement électronique menant à la supraconductivité. Grâce à ces résultats, un modèle est développé qui permet d’expliquer comment la température de transition critique est influencée par le changement des fré- quences de vibration du cristal. Ensuite, des résultats de calcul d’oscillations quantiques obtenus par une analyse approfondie de surfaces de Fermi, permettant une comparaison directe avec des données expérimentales, sont présentés dans deux articles. Le premier traite d’un matériau dans la famille des pnictures de fer, le LaFe2P2. L’absence de su- praconductivité dans ce matériau s’explique par la différence entre sa surface de Fermi obtenue et celle du supraconducteur BaFe2As2. Le second article traite du matériau à fermions lourds, le YbCoIn5. Pour ce faire, une nouvelle méthode efficace de calcul des fréquences de Haas-van Alphen est développée. Finalement, un dernier article traitant du cuprate supraconducteur à haute température critique YBa2Cu3O6.5 est présenté. À l’aide de la DFT+U, le rôle de plusieurs ordres magnétiques sur la surface de Fermi est étudié. Ces résultats permettent de mieux comprendre les mesures d’oscillations quan- tiques mesurées dans ce matériau. / In this thesis, the electronic structure of different kinds of superconductors is explored with the density functional theory. A brief explanation of this theory is done in the in- troduction. The Hubbard model is also presented as it can be used to solve shortcomings of the theory in some materials such as cuprates. The blend of the two theories is the DFT+U which is used to describe materials with strongly correlated electrons. After- ward, a paper describing the electron-phonon coupling in the superconductor NbC1−xNx is presented. Results from this work show the role of the Fermi surface in the electron pairing mechanism leading to superconductivity. Based on these results, a model is de- veloped explaining how the critical temperature is influenced by the change in frequency of the vibration modes. Then, quantum oscillation results based on a detailed analysis of Fermi surfaces, allowing a direct comparison with experimental data, are presented within two papers. The first one is about a material in the iron pnictide family, the LaFe2P2. Our calculations show that the Fermi surface of this material is different from the superconducting doped BaFe2As2 which explains why this material shows no sign of superconductivity. The second paper is about the heavy fermion system YbCoIn5. To do this, a new efficient method to calculate de Haas-van Alphen frequencies is developed. Finally, a paper on superconducting YBa2Cu3O6.5 is presented. Using DFT+U, the role of various magnetic orders on the Fermi surface are studied. The results allow a better understanding of the measured quantum oscillations in this material.

Les nanotubes de carbone et le graphène sont des nanostructures de carbone hybridé en sp2 dont les propriétés électriques et optiques soulèvent un intérêt considérable pour la conception d’une nouvelle génération de dispositifs électroniques et de matériaux actifs optiquement. Or, de nombreux défis demeurent avant leur mise en œuvre dans des procédés industriels à grande échelle. La chimie des matériaux, et spécialement la fonctionnalisation covalente, est une avenue privilégiée afin de résoudre les difficultés reliées à la mise en œuvre de ces nanostructures. La fonctionnalisation covalente a néanmoins pour effet de perturber la structure cristalline des nanostructures de carbone sp2 et, par conséquent, d’affecter non seulement lesdites propriétés électriques, mais aussi les propriétés optiques en émanant. Il est donc primordial de caractériser les effets des défauts et du désordre dans le but d’en comprendre les conséquences, mais aussi potentiellement d’en exploiter les retombées. Cette thèse traite des propriétés optiques dans l’infrarouge des nanotubes de carbone et du graphène, avec pour but de comprendre et d’expliquer les mécanismes fondamentaux à l’origine de la réponse optique dans l’infrarouge des nanostructures de carbone sp2. Soumise à des règles de sélection strictes, la spectroscopie infrarouge permet de mesurer la conductivité en courant alternatif à haute fréquence des matériaux, dans une gamme d’énergie correspondant aux vibrations moléculaires, aux modes de phonons et aux excitations électroniques de faible énergie. Notre méthode expérimentale consiste donc à explorer un espace de paramètres défini par les trois axes que sont i. la dimensionnalité du matériau, ii. le potentiel chimique et iii. le niveau de désordre, ce qui nous permet de dégager les diverses contributions aux propriétés optiques dans l’infrarouge des nanostructures de carbone sp2. Dans un premier temps, nous nous intéressons à la spectroscopie infrarouge des nanotubes de carbone monoparois sous l’effet tout d’abord du dopage et ensuite du niveau de désordre. Premièrement, nous amendons l’origine couramment acceptée du spectre vibrationnel des nanotubes de carbone monoparois. Par des expériences de dopage chimique contrôlé, nous démontrons en effet que les anomalies dans lespectre apparaissent grâce à des interactions électron-phonon. Le modèle de la résonance de Fano procure une explication phénoménologique aux observations. Ensuite, nous établissons l’existence d’états localisés induits par la fonctionnalisation covalente, ce qui se traduit optiquement par l’apparition d’une bande de résonance de polaritons plasmons de surface (nanoantenne) participant au pic de conductivité dans le térahertz. Le dosage du désordre dans des films de nanotubes de carbone permet d’observer l’évolution de la résonance des nanoantennes. Nous concluons donc à une segmentation effective des nanotubes par les greffons. Enfin, nous montrons que le désordre active des modes de phonons normalement interdits par les règles de sélection de la spectroscopie infrarouge. Les collisions élastiques sur les défauts donnent ainsi accès à des modes ayant des vecteurs d’onde non nuls. Dans une deuxième partie, nous focalisons sur les propriétés du graphène. Tout d’abord, nous démontrons une méthode d’électrogreffage qui permet de fonctionnaliser rapidement et à haute densité le graphène sans égard au substrat. Par la suite, nous utilisons l’électrogreffage pour faire la preuve que le désordre active aussi des anomalies dépendantes du potentiel chimique dans le spectre vibrationnel du graphène monocouche, des attributs absents du spectre d’un échantillon non fonctionnalisé. Afin d’expliquer le phénomène, nous présentons une théorie basée sur l’interaction de transitions optiques intrabandes, de modes de phonons et de collisions élastiques. Nous terminons par l’étude du spectre infrarouge du graphène comportant des îlots de bicouches, pour lequel nous proposons de revoir la nature du mécanisme de couplage à l’œuvre à la lumière de nos découvertes concernant le graphène monocouche. / Carbon nanotubes and graphene are sp2 hybridized carbon nanostructures which electrical and optical properties raise considerable interest for the design of a new generation of electronic devices and optically active materials. However, many challenges remain before their implementation in industrial processes on a large scale. Materials chemistry, especially covalent functionalization, is a privileged avenue to resolve the difficulties related to the processing of these nanostructures. Covalent functionalization, however, disrupts the sp2 carbon nanostructures’ crystalline structure, and pertubs not only said electrical properties, but also the deriving optical properties. It is therefore essential to characterize the effects of defects and disorder in order to understand their consequences, but also to potentially exploit the benefits. This thesis deals with the optical properties in the infrared of carbon nanotubes and graphene, with the aim to understand and explain the fundamental mechanisms at the origin of the optical response in the infrared of sp2 carbon nanostructures. Subject to strict selection rules, infrared spectroscopy measures the high frequency AC conductivity of materials in an energy range corresponding to molecular vibrations, phonon modes and low energy electronic excitations. Our experimental method is therefore to explore a parameter space defined by the three axes that are i. the dimensionality of the material, ii. the chemical potential, and iii. the disorder level, which allows us to identify the various contributions to optical properties in the infrared of sp2 carbon nanostructures. At first, we focus on the infrared spectroscopy of single-walled carbon nanotubes as a function of doping and disorder level. We start by amending the commonly accepted origin of single-walled carbon nanotubes vibrational spectra. Using controlled chemical doping experiments, we show that the anomalies in the carbon nanotube spectra appear through electron-phonon interactions. The Fano resonance model provides a phenomenological explanation for the observations. Then, we establish the existence of localized states induced by covalent functionalization, which appear as a surface plasmon polariton resonance (nanoantenna) contributing to the terahertz conductivity peak. Control of the disorder level in carbon nanotube films allows us to observe the evolution of the nanoantenna resonance. We therefore conclude to an effective segmentation of the nanotubes by the grafts. Finally, we show that disorder activates phonon modes that are usually forbidden by infrared spectroscopy’s selection rules. Disorder-induced infrared activity originates from elastic collisions on defects that give access to phonon modes with non-zero wave vectors. In a second part, we focus on the properties of graphene. First, we demonstrate an electrografting method to rapidly functionalize graphene with high-density, regardless of the substrate. Subsequently, we use electrografting to show that disorder activates chemical potential dependent anomalies in the vibrational spectra of single-layer graphene. These anomalies are absent in the spectra of pristine samples. In order to explain this phenomenon, we present a theory based on the interaction of intraband optical transitions, phonon modes and elastic collisions. We conclude by studying the infrared spectra of graphene with bilayer islands, for which we propose to review the nature of the coupling mechanism in the light of our findings on single-layer graphene.

Le graphène est une nanostructure de carbone hybridé sp2 dont les propriétés électroniques et optiques en font un matériau novateur avec un très large potentiel d’application. Cependant, la production à large échelle de ce matériau reste encore un défi et de nombreuses propriétés physiques et chimiques doivent être étudiées plus en profondeur pour mieux les exploiter. La fonctionnalisation covalente est une réaction chimique qui a un impact important dans l’étude de ces propriétés, car celle-ci a pour conséquence une perte de la structure cristalline des carbones sp2. Néanmoins, la réaction a été très peu explorée pour ce qui est du graphène déposé sur des surfaces, car la réactivité chimique de ce dernier est grandement dépendante de l’environnement chimique. Il est donc important d’étudier la fonctionnalisation de ce type de graphène pour bien comprendre à la fois la réactivité chimique et la modification des propriétés électroniques et optiques pour pouvoir exploiter les retombées. D’un autre côté, les bicouches de graphène sont connues pour avoir des propriétés très différentes comparées à la monocouche à cause d’un empilement des structures électroniques, mais la croissance contrôlée de ceux-ci est encore très difficile, car la cinétique de croissance n’est pas encore maîtrisée. Ainsi, ce mémoire de maîtrise va porter sur l’étude de la réactivité chimique du graphène à la fonctionnalisation covalente et de l’étude des propriétés optiques du graphène. Dans un premier temps, nous avons effectué des croissances de graphène en utilisant la technique de dépôt chimique en phase vapeur. Après avoir réussi à obtenir du graphène monocouche, nous faisons varier les paramètres de croissance et nous nous rendons compte que les bicouches apparaissent lorsque le gaz carboné nécessaire à la croissance reste présent durant l’étape de refroidissement. À partir de cette observation, nous proposons un modèle cinétique de croissance des bicouches. Ensuite, nous effectuons une étude approfondie de la fonctionnalisation du graphène monocouche et bicouche. Tout d’abord, nous démontrons qu’il y a une interaction avec le substrat qui inhibe grandement le greffage covalent sur la surface du graphène. Cet effet peut cependant être contré de plusieurs façons différentes : 1) en dopant chimiquement le graphène avec des molécules réductrices, il est possible de modifier le potentiel électrochimique afin de favoriser la réaction; 2) en utilisant un substrat affectant peu les propriétés électroniques du graphène; 3) en utilisant la méthode d’électrogreffage avec une cellule électrochimique, car elle permet une modulation contrôlée du potentiel électrochimique du graphène. De plus, nous nous rendons compte que la réactivité chimique des bicouches est moindre dû à la rigidité de structure due à l’interaction entre les couches. En dernier lieu, nous démontrons la pertinence de la spectroscopie infrarouge pour étudier l’effet de la fonctionnalisation et l’effet des bicouches sur les propriétés optiques du graphène. Nous réussissons à observer des bandes du graphène bicouche dans la région du moyen infrarouge qui dépendent du dopage. Normalement interdites selon les règles de sélection pour la monocouche, ces bandes apparaissent néanmoins lorsque fonctionnalisée et changent grandement en amplitude dépendamment des niveaux de dopage et de fonctionnalisation. / Graphene is a sp2 hybridized carbon nanostructure with incredible electronical and optical properties that make it interesting for various applications. Its large scale production is still a challenge and there is still some physical and chemical properties that need further studies to better exploit them. Covalent functionalization is a chemical reaction that can be used as a tool to study those properties because it breaks the sp2 crystalline structure, so it modulates the properties of graphene. There are not many studies of that reaction on graphene deposited on a surface because the chemical reactivity depends greatly on the chemical environment. That is why it is important to study the functionalization of graphene on surfaces to understand chemical reactivity and the modification of electronical and optical properties in order to potentially exploit the benefits. This master thesis is focusing on the chemical reactivity of graphene to covalent functionalization and the study of its optical properties. First, we grow graphene using the chemical vapour deposition method. After the growth of monolayer, we change the parameters and we observe the formation of bilayers if the carbonated gas is present during the cooling step of the growth. From that observation, we propose a kinetic model of bilayer growth. Then we proceed to a detailed study of monolayer and bilayer graphene functionalization. First, we demonstrate that there is a substrate effect that inhibits greatly the grafting of organic molecules on the graphene surface. However it is possible to overcome this substrate effect by different ways: 1) chemical doping of the graphene with reducing molecules can modify the electrochemical potential to enhance the reaction; 2) transferring graphene on a substrate that doesn’t affect the electronical properties of graphene; 3) the use of an electrografting method with an electrochemical cell can also modulate the potential so the efficiency of the reaction is enhanced. Also, we observe that the chemical reactivity of bilayer graphene is lower compared to the monolayer because of structural rigidity caused by interlayer interaction. Finally, we demonstrate that the infrared spectroscopy is a powerful tool to study the effect of functionalization and the effect of bilayers on the optical properties of graphene. We observe some bands in the region of the mid-IR, while the infrared selection rules don’t predict any. Also, the shape of those bands change greatly depending on the doping level when there is bilayers or when the graphene is functionalized.

Le formalisme des fonctions de Green hors-équilibre (NEGF pour « Non-equilibrium Green’s function) a suscité au cours des dernières décennies un engouement fort pour étudier les propriétés du transport quantique des nanostructures et des nano-dispositifs dans lesquels les interactions inélastiques, comme la diffusion des électrons-phonons, jouent un rôle significatif. L'incorporation d'interactions inélastiques dans le cadre du NEGF s’effectue généralement dans l'approximation auto-cohérente de Born (SCBA pour « Self-consistent Born approximation) qui représente une approche itérative plus exigeante en ressources numériques. Nous proposons dans ce travail de thèse une méthode efficace alternative dite LOA pour (« Lowest Order Approximation. Son principal avantage est de réduire considérablement le temps de calcul et de décrire physiquement la diffusion électron-phonon. Cette approche devrait considérablement étendre l'accessibilité de l'utilisation de codes atomistiques de transport quantique pour étudier des systèmes 3D réalistes sans faire à des ressources numériques importantes. / Non-equilibrium Green’s function (NEGF) formalism during recent decades has attracted numerous interests for studying quantum transport properties of nanostructures and nano-devices in which inelastic interactions like electron-phonon scattering have a significant impact. Incorporation of inelastic interactions in NEGF framework is usually performed within the self-consistent Born approximation (SCBA) which induces a numerically demanding iterative scheme. As an alternative technique, we propose an efficient method, the so-called Lowest Order Approximation (LOA) coupled with the Pade approximants. Its main advantage is to significantly reduce the computational time, and to describe the electron-phonon scattering physically. This approach should then considerably extend the accessibility of using atomistic quantum transport codes to study three-dimensional (3D) realistic systems without requiring numerous numerical resources.