The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction across a tunneling junction out of equilibrium

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic $s$-$d$ spin impurities across a tunneling junction is studied when the system is driven out of equilibrium through biasing the junction. The nonequilibrium situation is handled with the Keldysh time-loop perturbation formalism in conjunction with appropriate coupling methods for tunneling systems due to Caroli and Feuchtwang. We find that the presence of a nonequilibrium bias across the junction leads to an interference of several fundamental oscillations, such that in this tunneling geometry, it is possible to tune the interaction between ferromagnetic and antiferromagnetic coupling at a fixed impurity configuration, simply by changing the bias across the junction. Furthermore, it is shown that the range of the RKKY interaction is altered out of equilibrium, such that in particular the interaction energy between two slabs of spins scales extensively with the thickness of the slabs in the presence of an applied bias.Comment: 38 pages revtex preprint; 5 postscript figures; submitted to Phys. Rev.

Maximum-entropy theory of steady-state quantum transport

We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits

Time-Dependent Partition-Free Approach in Resonant Tunneling Systems

An extended Keldysh formalism, well suited to properly take into account the initial correlations, is used in order to deal with the time-dependent current response of a resonant tunneling system. We use a \textit{partition-free} approach by Cini in which the whole system is in equilibrium before an external bias is switched on. No fictitious partitions are used. Besides the steady-state responses one can also calculate physical dynamical responses. In the noninteracting case we clarify under what circumstances a steady-state current develops and compare our result with the one obtained in the partitioned scheme. We prove a Theorem of asymptotic Equivalence between the two schemes for arbitrary time-dependent disturbances. We also show that the steady-state current is independent of the history of the external perturbation (Memory Loss Theorem). In the so called wide-band limit an analytic result for the time-dependent current is obtained. In the interacting case we propose an exact non-equilibrium Green function approach based on Time Dependent Density Functional Theory. The equations are no more difficult than an ordinary Mean Field treatment. We show how the scattering-state scheme by Lang follows from our formulation. An exact formula for the steady-state current of an arbitrary interacting resonant tunneling system is obtained. As an example the time-dependent current response is calculated in the Random Phase Approximation.Comment: final version, 18 pages, 9 figure

DO TUNNELING ELECTRONS PROBE THE IMAGE INTERACTION ?

Some years ago Weinberg and Hartstein suggested that the discrepancy between their data on internal photoemission and photoassisted field emission was due to the inability of tunneling electrons to respond fully to the classical image potential. Since then much effort has been expended on explaining this as well as the more general problem of the effect of the full dynamical (i.e., velocity dependent quantum) image interaction on electron transport. However, neither problem has been definitively resolved. A major difficulty in the analyses using the classical image barrier has been the inability of over-simplified and inadequate models to explain observations in a manner consistent with the quantum mechanical limitations imposed on a tunneling electron. Specifically, the mean barrier approximations and the "image reduced" mean barrier are often imprecise approximations. Recently the logarithmic characteristics lnI (s;V = const) and lnV (s;I = const) have been determined using the STM. We have calculated lnI (s;V = const) for planar homo-junctions using two models with one-dimensional barriers, ϕ = ϕ (z) : (1) Simmons' mean barrier and hyperbolic approximations of the multiple image interaction, in the low bias limit, V ≪ ϕ0, the work function of the electrodes. (2) An exact integration of the Schrodinger equation to calculate the transmission across the full multiple image barrier. These calculations are discussed and compared with the experimental curves as well as some reported calculations by Binning et al

COMMENTS ON THE THEORY OF THE RESOLUTION IN THE SCANNING TUNNELING MICROSCOPE (STM) AND THE STRUCTURE OF THE TUNNELING BARRIER*

Une revue du STM et de son fonctionnement est présentée. L'évolution régulière et parfois déconcertante des modèles et de la machine et l'interprétation des résultats qui en résulte sont revus /1,3/. Il est démontré qu'une théorie réaliste du STM , qui serait consistente avec les théories multidimensionnelles habituelles de l'effet tunnel, doit inclure plusieurs points essentiels : 1) Une barrière de potentiel réaliste, à trois dimensions non séparables, qui doit tenir compte des interactions-images multiples et de la géométrie non plane de la jonction tunnel /4,5/. 2) Une définition opérationnelle du plan de surface de référence à partir duquel les déplacements de la pointe sont mesurés. 3) L'identification des quantités physiques réelles qui sont sondées par le STM / 6 / . 4) La définition de la résolution et l'analyse de ses limites pratiques. Dans ce papier, nous nous focalisons sur les points 4) et 1). Une revue des définitions conventionnelles de la résolution des microscopes /7/ révèle leur inapplicabilité au STM à cause de l'absence d'effets d'aberration et de grandissement dans les jonctions tunnel. Les trois définitions récemment proposées de la résolution du STM /1,3/ sont discutées de manière critique. Il est suggéré que contraste et résolution sont interdépendants et que les deux sont fortement affectés par la structure du potentiel tunnel. Bien plus, le diamètre effectif du "faisceau tunnel" et/ou de la structure émissive ne représente pas nécessairement la limite inférieure de résolution. L'impact de ces considérations sur la théorie et la conception du STM est considérée.A review of the STM and its operation is presented. The steady and occasionally baffling evolution of the models of the device and consequent interpretation of the data are reviewed /1,3/. It is argued that a realistic theory of the STM , which should be consistent with current multidimensional tunneling theory, must include several essential points : 1) A realistic and non-separable three-dimensional tunneling potential barrier, which has to account for the complete multiple image interaction and the non-planar geometry of the tunneling junction /4,5/. 2) An operational definition of the reference or surface plane, i.e., the surface from which the vertical displacement of the tip is measured. 3) Identification of the actual physical quantities being probed by the STM / 6 / . 4) Definition of resolution and analysis of its practical limits. In this paper we concentrate on points 4) and 1). A review of the conventiona1 definition of microscopes /7/ underscores their inapplicability to the STM because of the absence of lense aberrations and magnification effects in tunneling junctions. The three recently proposed definitions of the resolution in the STM /1,3/ are critically discussed. Alternatively, it is suggested that resolution and contrast are interrelated and that both are strongly affected by the structure of the tunneling potential. Furthermore, the effective diameter of the "tunneling beam" and/or the emitting structure (e.g., whisker) does not necessarily represent a lower bound for the resolution. The relevance of these considerations to the theory and design of the STM is considered

A MULTI-DIMENSIONAL TUNNELING THEORY WITH APPLICATION TO SCANNING TUNNELING MICROSCOPE

We have developed a formal general approach for evaluating the WKB wave function in a forbidden region of a non-separable potential in a three-dimensional space. The wave function is described by two sets of orthogonal wave-fronts, the equi-phase and equi-amplitude surfaces, or equivalently by two sets of paths defined to be normal to these surfaces respectively. We have extended a Huygens type construction to the forbidden region to obtain the multi-dimensional wave function. The construction determines the wave-fronts and the paths. It is found that the equations for the paths obtained from the construction are coupled to each other and do not reduce to a set of ordinary differential equations. However, if the incident wave is normal to the turning surface, the equations satisfied by the paths can be de-coupled. These equations are found to be equivalent to Newton's equations of motion for the inverted potential and energy. This characteristics has been used to calculate the current density distribution for an STM. In this paper, we use the same approach to derive the expressions for the lateral resolutions and corrugations for a model STM

SOLUTION OF LAPLACE'S EQUATION FOR A RIGID CONDUCTING CONE AND PLANAR COUNTER-ELECTRODE : COMPARISON WITH THE SOLUTION TO THE TAYLOR CONICAL MODEL OF A FIELD EMISSION LMIS

Bien que le problème électrostatique d'un cône conducteur rigide et d'une contre-électrode plane n'ait jamais été résolu exactement, nous montrons, en accordant les solutions à courte et à grande distance, que le champ au voisinage de l'apex est donné approximativement par : [MATH] Il est aussi démontré que la solution de Taylor au problème électrostatique d'un cône rigide et d'une contre-électrode plane ne satisfait pas l'équation de Laplace pour les configurations réelles d'électrodes utilisées dans les sources d'ions à métal liquide et dans d'autres expériences sur des fluides conducteurs soumis à des champs électrostatiques.Although the electrostatic problem of a rigid conducting cone and infinite planar counter-electrode has never been solved exactly, we show, by matching the near and far solutions, that the field in the vicinity of the apex is approximately given by [MATH] It is also explicitly demonstrated that Taylor's solution to the electrostatic problem of a rigid cone and non-planar counter-electrode model does not satisfy the Laplace Equation for the actual electrode configurations used in field emission liquid metal ion sources and other experiments on electrostatically stressed conducting fluids

THE EFFECTS OF GRAVITATIONAL AND HYDROSTATIC PRESSURE ON THE EQUILIBRIUM SHAPE OF A CONDUCTING FLUID IN AN ELECTRIC FIELD : APPLICATION TO LIQUID METAL ION SOURCES

We have derived a partial differential equation that can be solved explicitly for the equilibrium shape of an electrostatically stressed fluid subject to gravitational and hydrostatic pressure effects. The model assumes only axial symmetry, the Laplace stress conditions for mechanical equilibrium and conservation of volume before onset of instability. To obtain the sequence of deformed surfaces as a function of applied voltage, we use the capillary wave model and an iterative procedure to solve Laplace's equation for arbitrary geometry. Initial numerical results demonstrate the importance of pressure in obtaining stable equilibrium configurations

AN ELECTROHYDRODYNAMIC ANALYSIS OF THE EQUILIBRIUM SHAPE AND STABILITY OF STRESSED CONDUCTING FLUIDS : APPLICATION TO LMIS

Une analyse electrohydrostatique du modèle du cône de Taylor utilisant à la fois les critères de Taylor et de Zeleny fait ressortir plusieurs contradictions. On peut montrer qu'un traitement dynamique de la géométrie d'équilibre et de la stability peut en résoudre les contradictions apparentes. Et précisément, en utilisant l'équation electrodynamique linéarise et des corrections au 1st ordre, on montre qu'au seuil d'instabilité le cône prend une forme, "cuspidale". La tension critique de sevil d'instabilite est obtenue pour le gallium a partir de la relation de dispersion. La valeur calculee de 5.8 kV correspond bien aux mesures expérimentales de ~4-7 kV. Enfin, le caractère très localisé de l'instabilité est en accord avec les observations expérimentales obtenues en TEM par Sudraud, et. al.An electrohydrostatic analysis of the Taylor cone model, using both the Taylor and Zeleny stability criteria has revealed several inconsistencies in the model. It is shown that a dynamical treatment of the equilibrium shape and stability can resolve these apparent contradictions in the Taylor model. Specifically, using the linearized electrohydrodynamic equations with corrections up to first-order, it is shown that, at the onset of instability, the cone deforms into a cuspidal shape. From the dispersion relations, the critical voltage for the onset of instability is obtained for liquid gallium. The calculated value of 5.8 kV compares well with experimental values of ~4-7 kV. Finally, the instability is predicted to be highly localized, which agrees with the experimental observations in the TEM images or Sudraud, et. al