|
The charge transport properties of carbon nanotubes have been investigates intensively over the last years since they represent an archetype of a one-dimensional (1D) systems [1-3].
For metallic 1D systems, conventional Fermi-liquid theory fails due to strong correlation effects. Under certain conditions a 1D metal forms a Tomonaga-Luttinger liquid which shows
peculiar behavior such as spin charge separation and interaction dependent exponents in the density of states, correlation function, and momentum distribution of the electrons. The electronic density of states of the valence band electrons of mats of single-wall carbon nanotubes was directly monitored by angle integrated high resolution photoemission experiments.
The spectral function and the temperature dependence of the intensity at the Fermi level exhibited a power low dependence with the exponents of 0.46 and 0.48, respectively, which
are identical within experimental error. However, the observed exponent is much larger than the theoretical upper limit in the exact solvable Hubbard model, g =0.125, indicating that a more realistic microscopic model is required to describe the real quasi-1D systems.
The results of calculations of critical exponents obtained in the framework of a perturbation theory and the Luttinger liquid theory, where the electrons interact through the Coulomb interaction, lead to less values, since these approaches
are valid in the case of a weak interaction only. The questions arise: what is the electronic state that is realized in carbon nanotubes?
what is the nature of this state or what are the interactions, that lead to large values of the
critical exponents?
Note, that it is need to use the exact solvable models of strongly correlated electron systems for the description of this experimental phenomena, since calculations using the perturbation theory can not give large values of critical exponents theoretically. The purpose of the Report to propose the family of the exact solvable models of strongly correlated electron systems, calculate the critical exponents in the framework of the models proposed for the explanation of the phenomena. We will use the following arguments for construction of the models: 1. strong density-density correlations are realized at large values of the critical exponent g; 2. the dominating repulsive Coulomb interaction leads to strong density-density correlations in 1D electron liquid; 3. and finally, the hard-core Coulomb repulsive interaction leads to state of strongly interacting Luttinger liquid, that is characterized by large values of the critical exponent g. This has led us to propose a 'mechanism' of realization of phenomena based on exactly solvable many-body models with a hard-core repulsive interaction between particles. Using these ideas we will propose new family of exact solvable models that describe the electron state in carbon nanotubes with strong electron-electron interaction called as strongly interacting Luttinger liquid state. This state of electron liquid is characterized by large values of the critical exponents and the residual Fermi surface disappearing. In contrast to models studied previously, the long-distance behavior of correlation functions is described by strongly interacting Luttinger liquid state [4]. The photoemission experiments, obtained on the organic conductors, show much larger value of g =1.25 and g =1.5 than in carbon nanotubes where g =0.48. Such large values of the critical exponent g are explained in the framework of state strongly interacting Luttinger liquid, that is realized in 1D systems with a hard-core repulsive interaction between articles. The critical exponents of the correlation functions, that describe a power law behavior of the conductance and differential conductance with respect to temperature and bias voltage, are calculated using the Bethe ansatz solution of the model and conformal field theory. The model proposed to explain the experimental data for critical exponents observed on carbon nanotubes. 1. H. Ashii et al. Direct observation of Tomonaga-Luttinger-liquid state in carbon nanotubes at low temperatures, Nature 426, 540 (2003). 2. M. Bockrath et al. Luttinger liquid behavior in carbon nanotubes, Nature 397, 598 (1999). 3. A.K. Sood and S. Ghosh, Direct generation of a voltage and current by gas flow over carbon nanotubes and semiconductors, Phys. Rev. Lett. 93, 086601 (2004)). 4. I.N. Karnaukhov and A.A. Ovchinnikov, One-dimensional strongly interacting Luttinger liquid of lattice spinless fermions, Europhys.Lett. 57, 540 (2002). |