Spatially Resolved Manipulation of Single Electrons in Quantum Dots Using a Scanned Probe

Pioda, Alessandro; Kicin, Slavo; Ihn, Thomas; Sigrist, Martin; Fuhrer, Andreas; Ensslin, Klaus; Weichselbaum, Andreas; Ulloa, Sergio E.; Reinwald, Matthias; Wegscheider, Werner

doi:10.1103/physrevlett.93.216801

Cited by 110 publications

(116 citation statements)

References 23 publications

(23 reference statements)

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“…In scanning gate microscopy (SGM) [16,17], a charged tip is scanned above the device of interest, and the effect of the induced potential fluctuation on the conductance in the device is monitored. Over the past few years, scanning gate microscopy has been used to investigate transport phenomena in a variety of low-dimensional systems like quantum dots [18][19][20][21], quantum-point contacts [22], and two-dimensional electron gases [23][24][25][26]. Of particular relevance to QSH edge-state transport, SGM has been applied to one-dimensional systems like carbon nanotubes [27,28] and nanowires [29], where it was used to identify and manipulate localized states that control the transport through the device.…”

Section: Experimental Methodsmentioning

confidence: 99%

Spatially Resolved Study of Backscattering in the Quantum Spin Hall State

et al. 2013

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The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.

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Section: Experimental Methodsmentioning

confidence: 99%

Spatially Resolved Study of Backscattering in the Quantum Spin Hall State

et al. 2013

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“…The gate acts as a local electrostatic (repulsive or attractive) potential on the electronic system and allows to obtain two-dimensional (2D) conductance (or resistance) images of the scanned area as a function of the tip position. At the present time, SGM or an alternative technique called scanning capacitance microscopy (SCM) have been adopted to investigate the physics of quantum points contacts, 2,3,4,5,6 quantum dots, 7,8 carbon nanotubes, 9 open billiards 10 and edge states in the integer quantum Hall regime. 11,12,13,14 SGM on InAs nanowires has evidenced the presence of multiple quantum dots inside the structure corresponding to circular Coulomb blockade peaks in the conductance plots.…”

Section: Introductionmentioning

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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“…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) [2], Coulombblockaded quantum dots [3], magnetic focusing [4], carbon nanotubes [5], open billiards [6] and 2DEGs in the quantum Hall regime [7].…”

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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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Spatially Resolved Manipulation of Single Electrons in Quantum Dots Using a Scanned Probe

Cited by 110 publications

References 23 publications

Spatially Resolved Study of Backscattering in the Quantum Spin Hall State

Spatially Resolved Study of Backscattering in the Quantum Spin Hall State

Local density of states in mesoscopic samples from scanning gate microscopy

Imaging Electron Wave Functions Inside Open Quantum Rings

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