Electron transport in π-conjugated systems

Abstract: This thesis deals with theoretical studies of electron localization and conductance in conjugated molecular systems. Anderson localization of electrons is examined for nearly one-dimensional systems. This work was performed to understand the peculiar electronic properties of conducting polymers. The conductance through individual molecules has also been studied to improve the understanding of single molecule electronic devices.Localization of electrons in disordered materials has been studied extensively during the last decades. However, localization in nearly one-dimensional systems has partially been neglected. Conducting polymers is one important example of such a system. The peculiar temperature dependence of the conductivity of heavily doped conducting polymers has been attributed to disorder present in this type of systems. In the work presented in this thesis, the amount of disorder needed to localize the electronic wave function for conduction polymers has been calculated as a function of the doping level. The disorder studied includes chain breaks and on-site energy disorder. Using a one-electron Hückel description, the Lyapunov critical exponents of the conducting polymers were calculated. The localization length of the electronic wave function was thereafter found using finite size scaling. The amount of disorder needed to localize the wave function was shown to be much smaller for nearly one-dimensional system than for three-dimensional systems. This shows that conducting polymers are much more sensitive to disorder than previously expected. In the last few years physicists have managed to measure the electrical conductance through individual molecules. Theoretical models of the conductance have also been developed in parallel to the experimental studies. In the work presented in this thesis the Landauer formula has been used to calculate the current through molecules connected to metallic leads. The molecules studied range from buckminsterfullerene (C60 ) and nanotubes to simpler model systems. The size of the conductance is shown to depend crucially on the strength of the interaction between the metallic leads and the molecule. Interference and disorder are other effects that are important for the conductance.Electron-electron interactions were included in the conductance calculations using the Pariser-Parr-Pople Hamiltonian. This allowed calculations of the electrostatic potential drop over the molecule. The shape of the potential drop has been debated in the last years and our calculations show that the main part of the drop occurs at the molecule-lead junction. Charging of the molecule by the metallic leads was shown to affect the potential drop over the molecule. The charging results in a shift in the energy of molecular orbitals which in turn affects the resonance tunneling of electrons through the molecule. Since the current through the molecule mainly is due to resonance tunneling this has a large effect on the conductance. Negative differential resistance and asymmetric current-voltage characteristics have also been examined and explained in terms of charging of the molecule.