Critical study of perturbative approaches to tunneling

One of the long-lasting objectives of the theory of tunneling is to express the transmission probability in terms of the wave functions of infinitely separated electrodes. This can be achieved by the application of a perturbative approach to tunneling; in this context the transfer Hamiltonian method has been developed and used. In cases such as scanning tunneling microscopy operating at small tip-sample separation, however, it becomes necessary to go beyond the original transfer Hamiltonian method. In this study we examine the modified forms of the transfer Hamiltonian method using exactly solvable one-dimensional tunneling systems. We find that it is possible to calculate the transmission probability approximately by choosing appropriate boundary conditions for the wave functions used in the transition matrix element expression. However, for low and thin barriers these modified methods still fail to give the correct results. On the other hand, Green's-function techniques which extend the perturbation to all orders yield exact results irrespective of the boundary condition chosen at the interface. © 1992 The American Physical Society

Theoretical study of transport through a quantum point contact

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

Theory of anomalous corrugation of the Al(111) surface obtained from scanning tunneling microscopy

We provide an explanation of the observed anomalous corrugation of the Al(111) surface by calculating the current between the Al(111) sample and tip. An atomically sharp tip images the corrugation of the surface potential, which is enhanced by the tip-induced modifications of the electronic structure. At very small separations the effective barrier due to the lateral confinement of current-carrying states dominates the tunneling, however. This may lead to inversion of the corrugation. © 1990 The American Physical Society

Fano resonances in quasi-one-dimensional electron waveguides

In the spectroscopy of atoms and molecules, an asymmetric Fano resonance arises whenever a bound state associated with one electronic configuration is coupled to the ionization continuum of a different configuration. A strikingly similar resonance appears for electronic transport in conductors with more than one subband, independent of the specific details of the system under study. We develop a two-subband approximation which describes the Fano resonances for conduction through an electron waveguide containing donor impurities, for Γ-X-Γ intervalley tunneling in a GaAsAlxGa1-xAsGaAs heterojunction, and for an electron waveguide coupled to a resonant cavity. Interference between the direct and intersubband transmission channels gives rise to the asymmetric Fano resonance. © 1993 The American Physical Society

Effects of the constriction geometry on quasi-one-dimensional transport: Adiabatic evolution and resonant tunneling

The geometry of a constriction, which plays a crucial role in quasi-one-dimensional (quasi-D) ballistic transport, is investigated by performing calculations of the conductance. If the constriction becomes smoothly narrower inside, the current-carrying states evolve adiabatically leading to quantized conductance without a resonance structure. In contrast, quasi-0D (confined) states can form in a local widening inside the constriction and give rise to resonant tunneling. The effects of an obstacle at the entrance and the roughening along the constriction are also studied. © 1989 The American Physical Society

Novel features of quantum conduction in a constriction

The effects of the geometry and temperature on the quantum conductance for one-dimensional (1D) ballistic transport through a constriction in a 2D electron gas are investigated by use of a refined formalism. As the length of the constriction increases, weak oscillations around the classical conductance evolve into a steplike structure and the resonances on the plateaus become pronounced. Quantization at integer multiples of 2e2/h occurs only for uniform constriction of finite length. At finite temperature of 0.6 K significantly long uniform constriction is necessary to observe plateaus devoid of resonance structure. © 1989 The American Physical Society

Atomic theory of scanning tunneling microscopy

We present a quantitative analysis of the modifications of the scanning-tunneling-microscopy images due to the local perturbations of the electronic states induced by the tip in close proximity to the sample surface. Using an empirical tight-binding method, we have calculated the electronic states of a prototype tip-sample system consisting of a single-atom tip and the graphite surface, as a function of the tip-sample distance. We find that as the tip approaches the sample, their states start to interact and become laterally confined in the vicinity of the tip at small tip-sample separation. These states influence the tunneling phenomenon by connecting the tip and sample surface electronically. The effect of the tip-induced localized states is discussed, and the expression for the tunneling current is reformulated by incorporating the tip-induced states. Calculations using this expression show that the corrugation amplitude obtained from scanning tunneling microscopy is enhanced and deviates from the proportionality to the local density of states of the bare sample at the Fermi level evaluated at the center of the tip. © 1989 The American Physical Society

Potential oscillations near a barrier in the presence of phase-breaking scattering

Using the Greens function method for nonequilibrium processes, we study the potential oscillations near a barrier in both coherent- and incoherent-transport regimes. In the fully coherent regime the local electrochemical potential oscillates near the barrier, due to interference of the incident and reflected waves. The inclusion of phase-breaking scattering leads to suppression of these oscillations as a result of increasing contribution from the incoherent processes. As one goes away from the barrier, the amplitude of oscillations is found to decay with a decay length equal to the phase-scattering length. © 1992 The American Physical Society

Tip-structure effects on atomic force microscopy images

The authors study the effects of tip structure on images in atomic force microscopy by using a periodic force field fitted to ab-initio force calculations. 'Ideal' images resolving the sample atoms can be obtained with stable and atomically sharp tips in the repulsive range. In the weakly attractive range protrusions may occur at locations different from the atomic positions. Multiatom tips usually yield distorted images in which only the size and the shape of the sample unit cell is conserved. Rotation of a blunt tip or a finite flake lattice-matched to the sample causes stripes to form. Similar patterns can also appear for incommensurate sample-tip (or flake) systems

Ballistic transport through a quantum point contact: Elastic scattering by impurities

The effects of elastic scattering due to impurities in a quasi-one-dimensional constriction are investigated with an exact calculation of the conductance. It is found that the quantization of conductance is distorted owing to scattering by a single impurity which exists in an infinite constriction. The extent of deviation from quantized values depends on the strength, position, and lateral range of the scattering potential. The resonance structure due to interference of current-carrying waves is still apparent for a constriction of finite length containing an impurity. However, both the magnitude and position of these oscillations in the resonance structure are affected as a result of elastic scattering. A resonant tunneling effect is found due to a state bound to the attractive impurity potential. © 1990 The American Physical Society