Ballistic transport and tunneling in small systems

Ballistic transport and tunneling of electrons in mesoscopic systems have become one of the most important subjects of condensed matter physics. The quantum point contacts and scanning tunneling microscope form the basic experimental tools in this area and have been used for understanding many features of small systems. In this work ballistic transport and tunneling in small systems are investigated theoretically. Ballistic transport through narrow constrictions is investigated for a variety of configurations. It is found that for a uniform constriction the conductance is quantized in units of the quantum of conductance (2e^/A) for long channels. The interference of waves in the constriction gives rise to the resonance structure superimposed on the quantized steps. The lack of the resonance structure in the experimental results are attributed to temperature effects and/or adiabatic transport due to tapering of the constriction. It is shown that elastic scattering by an impurity distorts the quantization of conductance. Novel resonant tunneling effects due to formation of bound states are predicted for an attractive impurity or a local widening at the center of the constriction. It is shown that the probing in scanning tunneling microscopy have very much in common with narrow constrictions. The transition from tunneling to point contact regime is explained by the vanishing effective potential barrier as a result of tip-sample interaction. For noble and simple metals it is conjectured that lateral position dependent interaction between the tip and sample leads to corrugation of the potential barrier and in turn to atomic corrugation observed by scanning tunneling microscopy. The focused field emission of electrons from point sources is analyzed in a systematical way. The effective barrier due to the lateral confinement and nonadiabatic transport through the horn-like opening are found to be responsible for focusing. The nonequilibrium nature of transport is investigated by use of Keldysh Green’s function technique. The effects of elastic and inelastic scattering are analyzed in a strictly one-dimensional geometry. The features of voltage and current probes are studied and the Landauer formulae are examined for multiprobe measurements.