Conductance Through a Bent Carbon Nanotube

In this thesis a theoretical expression for the conductance through a bent nanotube is derived. The idea is inspired by a recent work by K. Flensberg and C. Markus, in which bent nanotubes are shown to be a prominent candidate for qubit realization [1]. An approximate Hamiltonian for graphene in the vicinity of the high-symmetry K(K′)-points is developed from the tightbinding model. An extension to carbon nanotubes, which are constructed from rolling up a graphene layer, is done using periodic boundary conditions. In addition, various perturbations are taken into account: the effect of a magnetic field, spin-orbit coupling, curvature induced hybridization and K(K′)-mixing. As a result, the energy bands split and the eigenstates become mixed. Assuming the tube to be locally straight, a bending in the translational direction is included through projection on to the local coordinate system of the tube segment. An integration routine for connecting the wavefunctions in the beginning and end of the tube is developed, such that a scattering matrix can be constructed, from which the transmission and reflection are deduced. From the Landauer formula the conductance can thus be determined. Using MATLAB, simulations of the transmission (conductance) as a function of the Fermi energy were performed for various tube geometries. Some of the simulations were haunted by unphysical fluctuations in the transmission and reflection which needs to addressed in a future study. However results indicating experimentally reported ballistic transport in nanotubes and quantized conductance steps in e2/h due to the energy splitting were observed. In addition, we found indication of resonance tunneling in certain nanotube geometries.