Tunneling times for one-dimensional systems

Gasparian, V.; Ortuño, M.; Ruiz, J.; Cuevas, E.; Pollak, M.

doi:10.1103/physrevb.51.6743

Cited by 30 publications

(34 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is clear that the oscillatory amplitude approach in general does not give the same answer as the GF formalism, based on the Larmor clock approach. As the difference between the corresponding tunneling times is proportional to the amplitude of reflection, we concluded that it arises from boundary effects [57].…”

Section: A Oscillatory Incident Amplitudementioning

confidence: 95%

“…This technique was already applied to obtain the traversal time [57] and the dwell time [86] of an arbitrary barrier. After some cumbersome algebra, using Eqs.…”

Section: Wavepacket Approachmentioning

confidence: 99%

“…Let us now derive a general expression for the Büttiker-Landauer traversal (and reflection) time using the Green's Function (GF) method [56,57]. We will consider a 1D system with an arbitrary potential V (y) confined to a finite segment 0 < y < L, as represented in fig.…”

Section: Formalism In Terms Of Green's Functionsmentioning

confidence: 99%

“…For a spatially symmetric barrier V ((L/2) + y) = V ((L/2) − y) the phase asymmetry ϕ a vanishes and one has additionally r = r . The integral of the GF at coinciding coordinates can be calculated quite generally in a finite region in terms of t and r (Aronov et al [58], Gasparian et al [57]). In appendix C we show how to perform this calculation.…”

Section: Expression In Terms Of Transmission and Reflection Amplitudesmentioning

confidence: 99%

“…(47) and (67), obtained with the GF formalism for the Larmor clock approach. The derivative with respect to the average height of the potential can be written in terms of partial derivatives with respect to energy E (Gasparian et al [57]). Thus the complex times τ V and τ V R are related to the real quantities τ BL z , τ BL y , τ BL y,R and τ BL z,R (see Eqs.…”

Section: General Barriermentioning

confidence: 99%

See 4 more Smart Citations

Tunneling time in nanostructures

Gasparian

Ortuño

Schön³

et al. 2000

Handbook of Nanostructured Materials and Nanotechnology

View full text Add to dashboard Cite

We review existing approaches to the problem of tunneling time, focussing on the Larmor clock approach. We develop a Green's function formalism and with it we are able to obtain close expressions for the tunneling and for the reflection times. A strong analogy between the results of the different approaches is established, and we show that their main differences are due to finite size effects. Furthermore we study the dwell time, and check that it can be exactly written as an average of one of the components of the traversal and the reflection times.We apply the results to a rectangular barrier, a periodic system and resonant tunneling, and we analyze the dependence of the tunneling time with the size of the wavepacket.We also discuss the recharging time in chemical nanostructures like ligand stabilized microclusters. We show that for nanoparticles with very small tunneling resistance RT ≤ 10 5 Ω it becomes to the same order of magnitude with tunneling time. CONTENTS

show abstract

Section: A Oscillatory Incident Amplitudementioning

confidence: 95%

“…This technique was already applied to obtain the traversal time [57] and the dwell time [86] of an arbitrary barrier. After some cumbersome algebra, using Eqs.…”

Section: Wavepacket Approachmentioning

confidence: 99%

Section: Formalism In Terms Of Green's Functionsmentioning

confidence: 99%

Section: Expression In Terms Of Transmission and Reflection Amplitudesmentioning

confidence: 99%

Section: General Barriermentioning

confidence: 99%

See 3 more Smart Citations

Tunneling time in nanostructures

Gasparian

Ortuño

Schön³

et al. 2000

Handbook of Nanostructured Materials and Nanotechnology

View full text Add to dashboard Cite

show abstract

On the application of the Kramers‐Kronig relations to the interaction time problem

Gasparian

Schön²,

Ruiz

et al. 1998

Annalen der Physik

View full text Add to dashboard Cite

It is shown that the two components of the complex characteristic interaction time τ(ω) = τ1(ω) — iτ2(ω) for classical electromagnetic waves with an arbitrary shaped barrier are not entirely independent quantities, but are connected by the Kramers‐Kronig relations. The corresponding macroscopic sum rule for the complex time is also derived. An analogy between the interaction time problem and an electrical circuit with capacitive and conducting components is established from which we propose that the effective crossing time should be the maximum of the two components.

show abstract

An analysis of the resonant tunneling‐time based on the presence‐time formalism

Barco¹

2007

Physica Status Solidi (b)

View full text Add to dashboard Cite

We analyze the tunneling-time of a spatial wave packet which traverses a resonant structure by means of the presence-time formalism. With this method we can evaluate the finite size effects of the corresponding energy probability distribution in the tunneling-time. We show that these effects are not negligible and reduce the tunneling-time by 25%. An expression for the resonant tunneling-time is derived, r 3 /2Γ , where r Γ is the width of the resonance. We confirm numerically this result for two resonant structures: a superlattice with n cells and square-barrier periodic potential, and an asymmetrical rectangular double-barrier potential.

show abstract

Tunneling times for one-dimensional systems

Cited by 30 publications

References 14 publications

Tunneling time in nanostructures

Tunneling time in nanostructures

On the application of the Kramers‐Kronig relations to the interaction time problem

An analysis of the resonant tunneling‐time based on the presence‐time formalism

Contact Info

Product

Resources

About