Dynamical effective potentials in electron tunneling: Path-integral study

Klipa, Nenad; Šunjić, Marijan

doi:10.1103/physrevb.52.12408

Cited by 9 publications

(15 citation statements)

References 27 publications

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“…We compare our results for V eff (6) with results obtained by a path integral technique [10][11][12] for the same model. In this paper, we do not rederive all the equations for the same conditions of electron-SP coupling.…”

Section: Path Integral Techniquementioning

confidence: 68%

“…Values for different definitions of the tunneling time through the barrier defined by the energy-dependent effective potential V eff (z, E). τ BL is given by (12), τ Ψ by (13), T by (10) and τ BL 0 is the Büttiker-Landauer tunneling time corresponding to the simple square barrier (no electron-SP interaction). The other parameters are V 0 = 0.4, L = 6, ω p = 0.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, we do not rederive all the equations for the same conditions of electron-SP coupling. Rather we refer to the paper of Klipa andŠunjić [12] and use their notation below. Within the path integral framework, the tunneling electron motion is described by the classical motion z(t) of the particle moving in the corresponding inverted effective potential V eff (z) :…”

Section: Path Integral Techniquementioning

confidence: 99%

“…For example, the dynamical image potential has been treated (i) classically [3, 4], (ii) within the selfenergy approach by non self-consistent [5, 6], semiclassical self-consistent [7] or fully self-consistent [8] calculations and (iii) by using a path integral technique [9][10][11][12].…”

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confidence: 99%

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Dynamical effective potential for tunneling: an exact matrix method and a path-integral technique

Ness

Fisher

1998

Applied Physics A: Materials Science & Processing

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The dynamical effective potential felt by an electron tunneling in a one-dimensional model STM junction is considered. The electron is coupled inside the barrier to surface plasmons. The corresponding many body Schrödinger equation is solved exactly by means of a matrix method. Results for the electron effective potential and for tunneling times are presented. They are compared to calculations for the same model barrier described within the path integral formalism. As is well known, significant differences from the corresponding static image potential are obtained when tunneling times are shorter than the inverse surface plasmon frequency. However, our results show that path integral calculations underestimate the tunneling traversal time, leading to a larger effective electron potential relative to that obtained by the matrix method.The actual conductance of an STM junction, with a given geometry and tip-sample separation, depends crucially on the potential felt by a tunneling electron [1,2]. A substantial contribution to this potential depends on the extent to which the tunnel junction is polarized by the electron's field. As well known, if tunneling is sufficiently slow (in comparison to the inverse surface plasmon frequency), the electron will feel the "image force" potential. If the tunneling is very rapid, however, the redistribution of the charge around the junction cannot occur sufficiently rapidly to build up the image charge.The dynamical aspects of the image potential have been studied by several authors within different approaches and approximations. For example, the dynamical image potential has been treated (i) classically [3, 4], (ii) within the selfenergy approach by non self-consistent [5, 6], semiclassical self-consistent [7] or fully self-consistent [8] calculations and (iii) by using a path integral technique [9][10][11][12].In this paper, we present a general matrix approach to treat the electron-plasmon coupling inside a tunneling junction. The corresponding many body Schrödinger equation is solved on a real-space mesh. We apply the method to a onedimensional model case and compare the results with those obtained within the path integral formalism for the same model. The modelsWe consider a model case where an electron tunnels through a static barrier V(r) between two planar metallic surfaces. Describing the metallic electrodes by a local scalar dielectric function, the electron is coupled, within the barrier, only to the surface plasmon (SP) modes. Each mode, of frequency ω ν and coupling matrix elements Γ ν (r), is characterized by a composite index ν = (q, α) where q is a vector parallel to the electrode surfaces and α = (±) represents the even and odd SP modes (i.e. in phase and out of phase oscillation of the charge on the two electrode surfaces).Due to the translation invariance parallel to the electrode surfaces, it is possible to recast the problem into a onedimensional system (only the motion of the electron perpendicular to the electrode surfaces is considered). The corresponding H...

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Section: Path Integral Techniquementioning

confidence: 68%

Section: Discussionmentioning

confidence: 99%

Section: Path Integral Techniquementioning

confidence: 99%

mentioning

confidence: 99%

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Dynamical effective potential for tunneling: an exact matrix method and a path-integral technique

Ness

Fisher

1998

Applied Physics A: Materials Science & Processing

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“…As shown in Refs. 16-18 even in this approximation the effective barrier ''rounds'' the edges of the static rectangular barrier, while in the presence of a finite electric field along the barrier, dynamical effects modify the transmission coefficient and barrier conductance, which has been shown by use of the pathintegral method 19 or the matrix method. 20 However, the fully self-consistent dynamical effective potential, calculated from the nonlocal self-energy, differs from the one obtained in the local approximation, 21,22 especially for narrow barriers (ϳ10 Å͒ which are becoming more and more technologically important.…”

Section: Introductionmentioning

confidence: 97%

Dynamical effects and conductance asymmetry in metal-insulator-metal systems with different electrodes

et al. 1999

Self Cite

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We investigated the electron tunneling process in a planar system consisting of two semi-infinite metal electrodes of different dielectric properties separated by a narrow vacuum gap. This system can be viewed as a model of a metal-insulator-metal structure, or even as a very rough model of scanning tunneling microscopy. We used a local limit of a self-consistent dynamic calculation to evaluate effective tunneling barriers, and discussed the influence of different screening properties of the metallic electrodes on these barriers as well as on the conductance. We found that the barriers are significantly additionally lowered due to the difference in the charge fluctuation frequencies of the electrodes, and that the conductance minimum in such systems is shifted to a nonzero value. We compared our results with some measurements of I-V characteristics and work functions and found that our calculations contribute to the understanding of the observed conductance asymmetry. ͓S0163-1829͑99͒06735-1͔

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Transition voltage spectroscopy in vacuum break junction: The standard tunneling barrier model and beyond

Bâldea

Köppel

2012

Physica Status Solidi (b)

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Recent experiments on transition voltage (V t ) spectroscopy in mechanically controllable vacuum break junctions have been interpreted theoretically by using a Simmons WKBtype approach of the transport by tunneling based on the standard vacuum barrier picture (work function þ source-drain bias þ charge images). In the first part of the paper, we present an analysis demonstrating the inconsistencies of that approach. Then, we report detailed results obtained by exactly solving the Schrödinger equation, which show that the standard tunneling barrier model fails to describe the experimental vacuum transition voltage spectroscopy (TVS) data. This indicates that the physical description within that model is incomplete. In the attempt to go beyond the standard barrier model, we report results demonstrating that the inclusion of electron states at the electrodes' surface significantly improves the agreement with experiment. This applies both to the d-dependence of V t and to the jump in the linear conductance when approaching the atomic contact limit.

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Dynamical effective potentials in electron tunneling: Path-integral study

Cited by 9 publications

References 27 publications

Dynamical effective potential for tunneling: an exact matrix method and a path-integral technique

Dynamical effective potential for tunneling: an exact matrix method and a path-integral technique

Dynamical effects and conductance asymmetry in metal-insulator-metal systems with different electrodes

Transition voltage spectroscopy in vacuum break junction: The standard tunneling barrier model and beyond

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