Electron Transport Through Nanoscopic Structures

This doctoral dissertation is concerned with modeling electron transport through nanoscopic structures, such as quantum dots, metal particles, or molecules. In Chapter 2, we consider statistical correlations between the heights of conductance peaks corresponding to two different levels in a Coulomb-blockaded quantum dot. Correlations exist for two peaks at the same magnetic field if the field does not fully break time-reversal symmetry as well as for peaks at different values of a magnetic field that fully breaks time-reversal symmetry. In Chapter 3, we present a density-matrix rate-equation approach to sequential tunneling through a metal particle weakly coupled to ferromagnetic leads. Our formalism is valid for an arbitrary number of electrons on the dot, for an arbitrary angle between the polarization directions of the leads, and with or without spin-orbit scattering on the metal particle. Interestingly, we find that the density-matrix description may be necessary even for metal particles with unpolarized leads if three or more single-electron levels contribute to the transport current and electron-electron interactions in the metal particle are described by the `universal interaction Hamiltonian'. In Chapters 4 and 5, we consider transport through molecular devices with strong coupling to a single vibrational mode for the case that the vibration is damped by coupling to the environment. We focus on the weak tunneling limit, for which a rate-equation approach is valid. The role of the environment can be characterized by a frequency-dependent frictional damping term and corresponding resonance frequency shift. We calculate current-voltage curves in Chapter 4 and find qualitative agreement between our theory and recent experiments on C_{60} single-molecule devices. In Chapter 5, we see that, depending on how the characteristic length scales of the van der Waals and electrostatic interaction of the molecule with the environment compare to each other, orthogonality catastrophe may appear or disappear, resulting in a smooth or discontinuous current-voltage curve, respectively. Finally, in Chapter 6, we investigate the influence of electron-phonon coupling on the current through a metallic single-walled carbon nanotube. In particular, we consider the high-energy optical and zone-boundary phonons and calculate an effective high-bias electron scattering rate, which is close to the experimentally observed value.Support by the Cornell Center for Materials Research (CCMR) under NSF grant no. DMR 0079992