Mechanically induced suppression of the conductance through telescopic carbon nanotubes

On December 29th 1959, Richard Feynman gave the celebrated talk ``There's Plenty of Room at the Bottom'' at the annual meeting of the American Physical Society at the California Institute of Technology. This talk is referred to by many as the prophetical ``incipit'' of the nanoscience era, which only thirty years later became experimental reality with the discovery of the scanning tunnel microscope [1]. In that talk Feynman stated [2]: $\lt$center> $\lt$table>$\lt$tr>$\lt$td width=400 align=justify> {\it But I am not afraid to consider the final question as to whether, ultimately -in the great future- we can arrange the atoms the way we want; the very atoms, all the way down! What would happen if we could arrange the atoms one by one the way we want them (within reason, of course; you can't put them so that they are chemically unstable, for example } $\lt$/td>$\lt$/tr>$\lt$/table> $\lt$/center> When looking at the discovery of carbon nanotubes (CNTs), it is difficult not to think of Feynman's words. Carbon nanotubes are in fact almost defect-free nanometer-scale tubules. One can visualize a carbon nanotube as a graphene stripe, rolled up into a seamless cylinder. Oberlin, Endo and Koyama produced TEM images of carbon nanotubes already in 1976 [3], but it was only in 1991 that Sumio Iijima [4], observing them as a byproduct in the synthesis of fullerenes, realized their potential and managed to produce them in bulk quantities. Since then, carbon nanotubes have constantly been in the intense focus of nanoelectronics research, due to the fact that they are expected to become an important component in molecular-scale devices [5]. But apart from their possible employment as material for the ``end of the semiconductor technology'', carbon nanotubes are an extraordinary playground for fundamental research. Carbon nanotubes allow to study the complex behavior of electrons in reduced dimensions as perfect quasi-one-dimensional and crystal-periodic systems. Due to their particular chemical structure, a reliable approximation used in the theoretical description of their electronic properties is based on the assumption that at the Fermi level the fourth p$_{z}$ valence electron of carbon, resulting in a $\pi$ orbital, mostly contributes to the electronic structure. Due to their chemical composition and the quasi-one-dimensional structure, carbon nanotubes have been predicted to have exceptional electronic and mechanical properties [6]: depending on the imposed boundary conditions on the graphene cutout one expects dramatically different electronic properties ranging from semiconducting to metallic behaviors. Metallic carbon nanotubes indeed bear current densities up to 10$^{7}$ A/cm$^{2}$. As it often happens with vital and revolutionary physical discoveries, many of the predictions regarding carbon nanotubes have already been confirmed in experiments [6-8]. Carbon nanotubes exist as single wall tubules (SWCNTs) or in coaxial multi wall configurations (MWCNTs). Both SWCNTs and MWCNTs have been reported to show ballistic transport even at room temperature. Regarding the mechanical properties of CNTs, besides of the potential application as the strongest and stiffest materials at the nanometer scale, the theoretically predicted ability of single shells in MWCNTs to easily slide and rotate with respect to each other, enforced the idea of novel nanodevices, based on the utilization of these mechanical degrees of freedom. The feasibility of nanojunctions made of telescopic nanotubes, such as nearly ideal linear and rotational nano-bearings and nano-springs, has been impressively confirmed in, among others, the experiments by Cumings and Zettl [9]. Double-walled carbon nanotubes (DWCNTs) were first observed by Dai {\it et al.} [10] and provide a perfect toy model for studying the properties of MWCNTs, such as the influence of the intershell-related mechanical degrees of freedom on quantum transport. This can be understood best by considering telescopic double wall carbon nanotubes (TDWCNTs). In TDWCNTs, the transport properties are affected by the intershell coupling, since the current path is interrupted by the overlapping region, the current being finally forced to flow between the layers. This thesis presents a systematic description of the calculations of the coherent and elastic charge transport properties of TDWCNTs. Confirmed in similar studies [12-14], the transport properties of TDWCNTs reveal interesting effects, such as the suppression of the conductance with increasing overlap lengths and a symmetry-driven conduction bands filter. These results suggest the possibility of tuning the transport properties of CNT-based junctions by using the available translational and rotational degrees of freedom. The presented thesis is organized according to the following plan: $\lt$ol>$\lt$li> {\it The physics of carbon nanotubes} Chapter 1 provides an introduction of the geometrical and electronic structure of SWCNTs and DWCNTs, starting from graphene. A brief overview of the synthesis methods is given and the hitherto existing insights on the exceptional mechanical properties of CNTs are presented. $\lt$/li>$\lt$li>{\it Special aspects of coherent quantum transport} Chapter 2 presents the tools needed for calculations of transport in systems ranging from the mesoscopic to the molecular scale. The usual theoretical approach to calculations of transport in CNTs is the Landauer formalism, providing a relation between the conductance and the transmission through the system. The transmission function can be obtained by using the scattering matrix technique, starting from a tight binding model approximation for the tube hamiltonian. Calculation techniques for transport in infinite periodic systems are presented as well. $\lt$/li>$\lt$li>{\it Mechanically tuned transport phenomena} The remaining part of this thesis work is an original work, focussing on transport phenomena emerging when {\it extended tunneling} occurs at the molecular scale. This was studied by means of TDWCNTs and a linear counterpart consisting in semi-infinite sliding chains. In Chapter 3, the transport properties of TDWCNTs as a function of different parameters, such as overlap length, rotation angle and energy, are introduced. Chapter 4 presents an effective model obtained by replacing each tube in a TDWCNT by a semi-infinite linear atomic chain. This model provides a large step towards the understanding of the exceptional transport effects in TDWCNTs. Also, an analytical expression for the transmission as a function of the overlap is obtained by means of a continuum model and proves to explain the armchair TDWCNTs phenomenology. $\lt$/li>$\lt$/ol