Single-wall carbon nanotubes (SWCNTs) are a fascinating material because they exhibit many outstanding properties. Due to their unique geometric structure, they are a paradigm for one-dimensional systems. Furthermore, depending on their chirality, they can be either metallic or semiconducting. The SWCNT are arranged in bundles of some ten nanotubes with a random distribution of semiconducting and metallic tubes. They are thus one-dimensional objects embedded in a three-dimensional arrangement, the bundles. In this thesis, the metallic ground state of one-dimensional (1D) and three-dimensional (3D) systems is investigated on the basis of SWCNTs, using angle-integrated photoemission spectroscopy. In particular, a transition from a 1D to a 3D metallic system, induced by a charge transfer, is studied on SWCNTs and C60 peapods. In general, the metallic ground state of materials is greatly influenced by correlation effects. In classical three-dimensional metals, electron-electron interaction mainly leads to a renormalization of the charge carrier properties (e.g. effective mass), as described in Landau's Fermi liquid theory. One-dimensional metals are influenced to a greater extent by interactions. In fact, the Landau-quasiparticle picture breaks down due to the Peierls instability. Instead, one-dimensional metals are described by Tomonaga-Luttinger liquid (TLL) theory which predicts unusual properties such as spin-charge separation and non-universal power laws in some physical properties such as the electronic density of states (DOS). Angle-integrated photoemission spectroscopy provides direct access to the DOS and as such directly addresses the power law renormalization of a TLL. It is first shown, that the bundles of single-wall carbon nanotubes indeed exhibit a power law scaling of the electronic density of states is observed as it is expected from TLL theory. The main part of the thesis is devoted to the investigation of the metallic ground state of SWCNTs upon functionalization. In general, functionalization is a controlled modification of the structural and/or electronic properties of SWCNT. It can be carried out e.g. by doping with electron donors or acceptors, by filling the nanospace inside the tubes with molecules or by substituting carbon atoms. First, the behavior of the SWCNT upon chemical doping was probed. The overall modification of the electronic band structure can be explained well by a rigid band shift model. The one-dimensional character of the metallic tubes in the bundle is retained at low doping, but when the semiconducting tubes in the sample are also rendered metallic by the charge transfer, a Fermi edge emerges out of the power law renormalization of the spectral weight, signifying a transition to a three-dimensional metallic behavior. This can be explained by an increased interaction between the tubes in the bundle. A crossover from a Tomonaga-Luttinger liquid to a Fermi liquid is observed. The filling of SWCNTs with C60 molecules leads to the formation of so-called peapods. It raises questions concerning the role of the additional bands originating from the C60 filling in the one-dimensional system. In the pristine state, the states of the C60 filling were found to have no influence on the metallic ground state. The TLL power law scaling of the density of states is observed. The overall interaction between the SWCNT host and the C60 filling is small. Upon doping however, the modified band structure leads to a qualitative change in the crossover from a TLL to a Fermi liquid. Upon doping, also states in the conduction band of the C60 are filled. The evolution of the power law scaling at intermediate doping can be interpreted as an opening of an additional conduction channel of one-dimensional metallic chains of C60 inside the tubes. This is in good agreement with transport experiments. Upon further doping, a Fermi edge similar to the highly doped SWCNTs is observed.

Single-wall carbon nanotubes (SWCNTs) are a fascinating material because they exhibit many outstanding properties. Due to their unique geometric structure, they are a paradigm for one-dimensional systems. Furthermore, depending on their chirality, they can be either metallic or semiconducting. The SWCNT are arranged in bundles of some ten nanotubes with a random distribution of semiconducting and metallic tubes. They are thus one-dimensional objects embedded in a three-dimensional arrangement, the bundles. In this thesis, the metallic ground state of one-dimensional (1D) and three-dimensional (3D) systems is investigated on the basis of SWCNTs, using angle-integrated photoemission spectroscopy. In particular, a transition from a 1D to a 3D metallic system, induced by a charge transfer, is studied on SWCNTs and C60 peapods. In general, the metallic ground state of materials is greatly influenced by correlation effects. In classical three-dimensional metals, electron-electron interaction mainly leads to a renormalization of the charge carrier properties (e.g. effective mass), as described in Landau's Fermi liquid theory. One-dimensional metals are influenced to a greater extent by interactions. In fact, the Landau-quasiparticle picture breaks down due to the Peierls instability. Instead, one-dimensional metals are described by Tomonaga-Luttinger liquid (TLL) theory which predicts unusual properties such as spin-charge separation and non-universal power laws in some physical properties such as the electronic density of states (DOS). Angle-integrated photoemission spectroscopy provides direct access to the DOS and as such directly addresses the power law renormalization of a TLL. It is first shown, that the bundles of single-wall carbon nanotubes indeed exhibit a power law scaling of the electronic density of states is observed as it is expected from TLL theory. The main part of the thesis is devoted to the investigation of the metallic ground state of SWCNTs upon functionalization. In general, functionalization is a controlled modification of the structural and/or electronic properties of SWCNT. It can be carried out e.g. by doping with electron donors or acceptors, by filling the nanospace inside the tubes with molecules or by substituting carbon atoms. First, the behavior of the SWCNT upon chemical doping was probed. The overall modification of the electronic band structure can be explained well by a rigid band shift model. The one-dimensional character of the metallic tubes in the bundle is retained at low doping, but when the semiconducting tubes in the sample are also rendered metallic by the charge transfer, a Fermi edge emerges out of the power law renormalization of the spectral weight, signifying a transition to a three-dimensional metallic behavior. This can be explained by an increased interaction between the tubes in the bundle. A crossover from a Tomonaga-Luttinger liquid to a Fermi liquid is observed. The filling of SWCNTs with C60 molecules leads to the formation of so-called peapods. It raises questions concerning the role of the additional bands originating from the C60 filling in the one-dimensional system. In the pristine state, the states of the C60 filling were found to have no influence on the metallic ground state. The TLL power law scaling of the density of states is observed. The overall interaction between the SWCNT host and the C60 filling is small. Upon doping however, the modified band structure leads to a qualitative change in the crossover from a TLL to a Fermi liquid. Upon doping, also states in the conduction band of the C60 are filled. The evolution of the power law scaling at intermediate doping can be interpreted as an opening of an additional conduction channel of one-dimensional metallic chains of C60 inside the tubes. This is in good agreement with transport experiments. Upon further doping, a Fermi edge similar to the highly doped SWCNTs is observed.

Dans cette thèse nous avons étudié les fluctuations de courant, l'admittance quantique ainsi que la densité d'états pour un nano système en interaction. Dans la première partie de la thèse, nous avons étudié les fluctuations de courant et l'admittance pour un conducteur unidimensionnel, en décrivant le système par un liquide de Tomonaga-Luttinger. Les techniques de bosonisation et de refermionisation permettent d'avoir des résultats exacts. Ces résultats sont appliqués à un conducteur cohérent couplé à un quantum de résistance, et aux états de bord dans le régime de l'effet Hall quantique fractionnaire. Dans le cas d'un conducteur cohérent, le bruit non symétrisé à fréquence finie exhibe un profil différent de celui de la théorie de la diffusion, et la conductance à fréquence finie est directement liée au courant. Dans le cas des états de bord, nous avons établi une relation entre les corrélations de courant et l'admittance dans certaines limites. En particulier, les singularités qui apparaissent dans les corrélations de courant sont celles de l'admittance. Dans la deuxième partie, nous avons étudié un fil quantique connecté à deux réservoirs représentés par deux impuretés. Le système est décrit par un liquide de Tomonaga-Luttinger. Nous avons établi et résolu l'équation de Dyson pour la fonction de Green retardée. Ce qui permet de calculer la densité d'états pour un fil quantique homogène puis inhomogène. Dans le cas d'un paramètre d'interaction homogène, l'effet des impuretés modifie le profil de la densité d'états. Dans le cas d'un paramètre d'interaction inhomogène, le calcul de la densité d'états est plus difficile et une approche numérique est indispensable. / In this thesis we focus on the study of the current fluctuations, quantum admittance and density of states of an interacting nano system. The first part of the thesis is related to the calculation of current fluctuations and admittance for one dimensional conductor. The system is described by a Tomonaga-Luttinger liquid. The use of bosonization and refermionization procedures allows us to obtain exact results, valuable whatever the value of the applied voltage, for all frequencies and all temperature regimes. Tow cases are studied. In the first one, we consider a coherent conductor coupled to a quantum of resistance. We find that the finite frequency noise behavior differs from that of the scattering theory, and the finite frequency conductance is directly related to the current. In the second case, we study edge states in the fractional quantum Hall regime. We establish a relationship between the current correlations and the admittance in certain limits. Thus, the singularities observed in the current correlations are those of the admittance. The second part of the thesis is devoted to the study of an interacting quantum wire connected to tow leads modeled as two impurities. The system is described by a Tomonaga-Luttinger liquid. We derived and solved an exact Dyson equation for a retarded Green function. Than we calculate the density of states in two cases, homogeneous quantum wire, and next inhomogeneous one. The effect of the impurities changes the behavior of the density of states for the homogeneous case. In the case of a position depending interaction parameter, the calculation of the density of states is more difficult and a numerical approach is needed.