Transport in Nanoscale Systems

In part I of the Thesis charge ordering and transport in arrays of coated semiconductor nanocrystals (quantum dot arrays) are studied. Charge ordering in dot arrays is considered by mapping the electrons on the dots onto the frustrated spin model on the triangular lattice. A number of phases is identified for this system. Phase diagram is studied by means of the height field order parameter. Novel correlated fluid phase is identified, in which transport of classical charges exhibits correlated behavior. Freezing transitions into commensurate ground state configurations are found to be of the first order. A novel model of transport in disordered systems is proposed to account for experimentally observed current transients in dot arrays at high bias. This transport model yields a non-stationary response in a stationary system. The model proposes a particular power law noise spectrum that is found to be consistent with experiments. In Part II of the Thesis novel effects in Carbon nanotubes are predicted. These effects can be manifest in transport measurements. First, it is shown that a strong electric field applied perpendicularly to the tube axis can fracture the Fermi surface of metallic nanotubes and significantly reduce excitation gap in semiconducting nanotubes. The depolarization problem is linked to the chiral anomaly of 1+1 dimensional Dirac fermions. Second, coupling between a surface acoustic wave and nanotube electrons is proposed as a means to realize an adiabatic charge pump. Incompressible states are identified in the single particle picture, and the corresponding minigaps are found. Conditions for pumping experiment are identified. Third, electron properties of a nanotube in a periodic potential are considered. It is shown that when the electron density is commensurate with the potential period, incompressible electron states exist. Electron interactions are treated in the Luttinger liquid framework, and excitation gaps corresponding to incompressible states are found using the phase soliton approach. Thesis Supervisor: Leonid S. Levitov Title: Professor of Physics