Measurement of the tip-induced potential in scanning gate experiments

Gildemeister, A. E.; Ihn, Thomas; Sigrist, Martin; Ensslin, Klaus; Driscoll, D. C.; Gossard, A. C.

doi:10.1103/physrevb.75.195338

Cited by 45 publications

(65 citation statements)

References 20 publications

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“…Notice that the spatial extension of such a potential is larger than 2σ. However, since recent experimental results on open quantum dots have pointed out that, in some cases, a significant spatial asymmetry characterizes the tip-induced potential, 22 we have also adopted an asymmetric shape for U (x, y). In Figs.…”

Section: Figmentioning

confidence: 99%

Local density of states in mesoscopic samples from scanning gate microscopy

et al. 2008

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We study the relationship between the local density of states (LDOS) and the conductance variation ∆G in scanning-gate-microscopy experiments on mesoscopic structures as a charged tip scans above the sample surface. We present an analytical model showing that in the linear-response regime the conductance shift ∆G is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers-Kronig relation holds between LDOS and ∆G. We analyze the physical conditions for the validity of this relationship both for one-dimensional and two-dimensional systems when several channels contribute to the transport. We focus on realistic Aharonov-Bohm rings including a random distribution of impurities and analyze the LDOS-∆G correspondence by means of exact numerical simulations, when localized states or semi-classical orbits characterize the wavefunction of the system.

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Section: Figmentioning

confidence: 99%

Local density of states in mesoscopic samples from scanning gate microscopy

et al. 2008

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“…To investigate further on the SGM imaging mechanism, we need to examine the influence of a key ingre- dient: the perturbing potential [11]. Experimentally, a way to control this parameter is to change the tip voltage.…”

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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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“…carbon nanotubes, 6 quantum rings, 7,8 InAs nanowires, 9 and quantum dots 10,11 ) and can be caused by a tip-induced modulation of either quantum interference 7 or Coulomb blockade (CB). 6,9-11 Indeed, both mechanisms can be expected to play a role in artificial AD devices, as highlighted by a number of investigations in past years reviewed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Imaging backscattering through impurity-induced antidots in quantum Hall constrictions

et al. 2012

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We exploit the biased tip of a scanning gate microscope (SGM) to induce a controlled backscattering between counter-propagating edge channels in a wide constriction in the quantum Hall regime. We compare our detailed conductance maps with a numerical percolation model and demonstrate that conductance fluctuations observed in these devices as a function of the gate voltage originate from backscattering events mediated by localized states pinned by potential fluctuations. Our imaging technique allows us to identify the necessary conditions for the activation of these backscattering processes and also to reconstruct the constriction confinement potential profile and the underlying disorder.

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Measurement of the tip-induced potential in scanning gate experiments

Cited by 45 publications

References 20 publications

Local density of states in mesoscopic samples from scanning gate microscopy

Local density of states in mesoscopic samples from scanning gate microscopy

Imaging Electron Wave Functions Inside Open Quantum Rings

Imaging backscattering through impurity-induced antidots in quantum Hall constrictions

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