Theoretical study of transport through a quantum point contact

Abstract

We developed a formalism within the linear-response theory to investigate the transport through a quantum point contact between two electron-gas reservoirs. It is valid for two-terminal conductance through a constriction of a two-dimensional (2D) or 3D potential and has a wide range of applicability covering ballistic as well as tunneling regimes. We studied the quantization of conductance and examined several effects influencing the quantum transmission. Among these effects we found that the simple phase relation results in resonance structures superimposed on the plateaus between two steps of quantized conductance. These resonances are destroyed by the smooth entrance, finite temperature and bias, and variation of the potential. The simulation of adiabatic transmission in constrictions having smoothly varying widths resulted in the conductance with sharp quantum steps without the resonance structure. The quality of quantization is strongly affected by the length of constriction, Fermi-level smearing, the obstacle at the entrance, impurity scattering, nonuniformities of geometry and potential, and in particular by the variation of the longitudinal potential resulting in a sharp saddle-point structure. The quasibound states may occur in a local widening of the width or in a locally lowered potential. These states give rise to a sudden increase of the transmission prior to the opening of a new conduction channel. We present an extensive analysis of this phenomenon and show that it is due to resonant tunneling through these bound states. Owing to enhanced backscattering, the bound states of an attractive impurity in a constriction can yield dips in the conductance at the threshold of channels. In addition to quantized ballistic transport, we extended our method to treat the transport mechanism in scanning tunneling microscopy and in field emission of collimated electrons from an atomic-size source. The issues of current interest in these fields that we treated are (i) the transition from the tunneling to the ballistic regime and the interpretation of conductance oscillations, and (ii) the anomalous corrugation of flat metal surfaces. Our results reveal crucial features of the lateral confinement of the current-transporting states in the constriction of potential between the tip and sample. The effective barriers created from this confinement effect dominate the transmission at small tip-sample distances and influence the apparent barrier height. © 1991 The American Physical Society.