Electronic properties of carbon nanotube structures

An individual single-wall carbon nanotube has a periodic structure. Despite that, and because nanotubes can have different chiralities, systems of nanotubes can be highly non-periodic. This implies some difficulty in studying the electronic properties of nanotube structures. In this thesis, three nanotube systems are studied.; The first problem presented in this thesis is that of a compositionally disordered nanotube rope. Using a tight binding approach, we derive a tunneling matrix element that couples low-energy electronic states of carbon nanotubes. The matrix element Dependence on chiral angles and intratube crystal momenta is explicitly shown. We find that conservation of crystal momentum along the tube direction suppresses interwall coherence in a carbon nanorope containing tubes with random chiralities. Numerical calculations are presented which indicate that electronic states in a rope are localized in the transverse direction with a coherence length corresponding to a tube diameter.; The second problem we study is that of a junction made of two crossed metallic nanotubes of general chiralities. We derive a tunneling matrix element that couples low-energy states on the two tubes, allowing us to calculate the contact conductance of the junction. We systematic study the dependence of the junction conductance on different junction parameters, and find that the crossing angle has the dominant effect on the conductance magnitude. Furthermore, and because of the intrinsic asymmetries of the junction, forward and backward hopping probabilities from one nanotube to another are different. As a result, passing a current in one tube leads to a finite voltage drop across the other, thereby ascribing a zero-field Hall-like resistance to the junction. We find that this Hall resistance and the contact resistance of the junction are simply related.; Our third problem is aimed at understanding the scanning tunneling microscopy (STM) energy-resolved images of finite chiral metallic nanotubes. The STM technique is a powerful one, as it allows for the study of the electronic and structural properties of carbon nanotubes. Of recent interest is the STM imaging of discrete states of finite metallic nanotubes. In order to understand such images, we consider two effects. The first is that the reflection at the ends of the nanotube mixes the two nanotube bands in a non-universal way, yielding two families of eigenstates. The second effect is that of the STM tip. Images of the wavefunctions can be dramatically changed by the STM tip. We show that by analyzing the STM images of the two families of states, one can extract the tip effects and obtain information about the wavefunctions of the two families.