Optical Analogy to Electronic Quantum Corrals

Francs, Gérard Colas des; Girard, Christian; Weeber, Jean-Claude; Chicane, Cédric; David, T.; Dereux, Alain; Peyrade, D.

doi:10.1103/physrevlett.86.4950

Cited by 100 publications

(92 citation statements)

References 18 publications

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“…Using quantum mechanical simulations of the electron probability density, including the perturbing potential of the tip, we could reproduce the main experimental features and demonstrate the relationship between conductance maps and electron probability density maps. Hence, one can view SGM as the analog of STM for imaging the electronic LDOS in open mesoscopic systems buried under an insulating layer, or the counterpart of the near-field scanning optical microscope that images the photonic LDOS in confined nanostructures [19]. …”

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confidence: 99%

Imaging Electron Wave Functions Inside Open Quantum Rings

et al. 2007

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Combining Scanning Gate Microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of electron probability density |Ψ| 2 (x, y) in embedded mesoscopic quantum rings (QRs). The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wavefunction interferences. Simulations of both |Ψ| 2 (x, y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Ψ| 2 (x, y). Thanks to the scanning tunnelling microscope (STM), remarkable precision has been achieved in the local scale imaging of surface electron systems. Only a few years after the STM invention, electron interferences could be visualized in real space inside artificially confined surface structures, the "quantum corrals" [1]. However, since they rely on the measurement of a current between a tip and the sample, STM techniques are useless when the system of interest is buried under an insulating layer, as in two-dimensional electron gases (2DEGs) confined in semiconductor heterostructures. To circumvent the obstacle, a new method was developed: the Scanning Gate Microscopy (SGM). SGM consists in mapping the conductance of the system as the polarized tip, acting as a flying nano-gate, scans at a constant distance above the 2DEG. SGM gave many valuable insights into the physics of quantum point contacts (QPCs) [7].[In some cases, the mechanism of SGM image formation is readily understandable. For example, in the vicinity of a QPC [2], coherent electron flow is imaged due to multiple reflections and interferences of electrons bouncing between the QPC and the tip-induced depleted region. In comparison, the situation seems more complex when the tip scans directly over an open mesoscopic billiard [6]: the tip perturbation extends over the whole system of interest, so that all semi-classical trajectories are modified. The mechanisms that link conductance maps to the properties of unperturbed electrons still need to be clarified. Recently, we showed that SGM images in the vicinity of a QR allow direct observation of iso-phase lines for electrons in an electrostatic Aharonov-Bohm (AB) experiment [8].In this Letter, we discuss SGM images obtained as the tip scans directly over coherent quantum rings (QRs). Experimentally, we find that the amplitude of conductance modulations shares a common temperature dependence with the Aharonov-Bohm effect, a direct evidence that SGM probes the quantum nature of electrons. On the other hand, we perform quantum mechanical simulations of SGM experiments. First, the amplitude of conductance fringes is found to evolve linearly at low perturbation amplitude, both in experiments and simulations. Second, we observe a direct correspondence between simulated SGM data and simulations of the electron probability density |Ψ| 2 (x, y, E F ). We deduce that, in this linear regime, SGM reliably maps |Ψ| 2 (x, y, E F ) in coherent QRs.We fabricated two QRs, samples R1 and R2, from an InGa...

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Imaging Electron Wave Functions Inside Open Quantum Rings

et al. 2007

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“…For this purpose, we now establish a relationship between 2D and 3D LDOS by introducing Green's dyad formalism. First, the 3D-LDOS is related to the 3D Green's tensor G of the system (Im and T r refer to the imaginary part and trace) [17] ρ(r) = − k 2 0 πω ImT rG(r, r) .…”

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Purcell factor for a point-like dipolar emitter coupled to a two-dimensional plasmonic waveguide

et al. 2011

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We theoretically investigate the spontaneous emission of a point-like dipolar emitter located near a two-dimensional (2D) plasmonic waveguide of arbitrary form. We invoke an explicite link with the density of modes of the waveguide describing the electromagnetic channels into which the emitter can couple. We obtain a closed form expression for the coupling to propagative plasmon, extending thus the Purcell factor to plasmonic configurations. Radiative and non-radiative contributions to the spontaneous emission are also discussed in details.

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“…It is an intrinsic electromagnetic quantity of the object, independent on the excitation process. For instance the local density of mode is given by [24,25] …”

Section: Green's Dyadic Techniquementioning

confidence: 99%

Near-Field Properties of Plasmonic Nanostructures With High Aspect Ratio

Agha¹,

Demichel²,

Girard³

et al. 2014

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Abstract-Using the Green's dyad technique based on cuboidal meshing, we compute the electromagnetic field scattered by metal nanorods with high aspect ratio. We investigate the effect of the meshing shape on the numerical simulations. We observe that discretizing the object with cells with aspect ratios similar to the object's aspect ratio improves the computations, without degrading the convergency. We also compare our numerical simulations to finite element method and discuss further possible improvements.

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Optical Analogy to Electronic Quantum Corrals

Cited by 100 publications

References 18 publications

Imaging Electron Wave Functions Inside Open Quantum Rings

Imaging Electron Wave Functions Inside Open Quantum Rings

Purcell factor for a point-like dipolar emitter coupled to a two-dimensional plasmonic waveguide

Near-Field Properties of Plasmonic Nanostructures With High Aspect Ratio

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