Scanning Single-Electron Transistor Microscopy: Imaging Individual Charges

Yoo, Myong Jae; Fulton, T. A.; Hess, Harald F.; Willett, R. L.; Dunkleberger, L. N.; Chichester, R. J.; Pfeiffer, L. N.; West, K. W.

doi:10.1126/science.276.5312.579

Cited by 284 publications

(175 citation statements)

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“…Details of our experimental method are described in Ref. [31,32]. The diameter of the SET is about 100 nm and the distance between SET and the sample is roughly 50 nm.…”

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confidence: 99%

Observation of electron–hole puddles in graphene using a scanning single-electron transistor

et al. 2007

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The electronic density of states of graphene is equivalent to that of relativistic electrons [1-3]. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities [4-6], many questions pertaining to disorder [7-14] remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically [13]. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions. The kinetic energy of Dirac particles in graphene increases linearly with momentum [1,15,16]. The total energy per particle however, also referred to as the chemical potential, µ , contains additional exchange and correlations contributions that arise from the Coulomb interactionHere K E , ex E and c E are the kinetic, exchange and correlation terms respectively. Therefore, the chemical potential and its derivative with respect to density, known as the inverse compressibility or density of states, provide direct insight into the properties of the Coulomb interaction in such a system. Compressibility measurements of conventional, massive, two dimensional electron systems made for example of Si or GaAs have been carried out by several groups [19,[23][24][25][26]. It has been shown that at zero magnetic field the chemical potential may be described rather accurately within the Hartree-Fock approximation. Quantitatively it has been found that Coulomb interactions add a substantial contribution to the compressibility and become dominant at low carrier densities. In a perfectly uniform and clean graphene sample, the inverse compressibility is expected to diverge at the Dirac point in view of the vanishing density of states. This divergence, however, is expected to be rounded off by disorder on length scales smaller than our tip size. Long range disorder on the other hand will cause local shifts in the Dirac point indicative of a non-zero local density. In this work we measure the spatial dependence of the local compressibility versus carrier density across the sample. Fluctuations in the Dirac point across the sample are translated into

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“…Details of our experimental method are described in Ref. [31,32]. The diameter of the SET is about 100 nm and the distance between SET and the sample is roughly 50 nm.…”

mentioning

confidence: 99%

Observation of electron–hole puddles in graphene using a scanning single-electron transistor

et al. 2007

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“…The DC voltage on the tip perturbs the carrier density in the sample by less than 10% [24], as estimated from scanned gate measurements [25], but changing the density perturbation from about 5% to 25% does not qualitatively affect the observations reported below. Note also that height and contact potential fluctuations [26] cause local variations in the signal strength. We account for these by normalizing the measured signal with a simultaneously-measured reference signal whereby a uniform voltage is applied to all contacts on the sample.…”

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confidence: 99%

Scanned potential microscopy of edge and bulk currents in the quantum Hall regime

et al. 1999

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Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. In addition, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk currents in the QH regime.PACS numbers: 73.40. Hm, 61.16.Ch, Since the discovery of the quantum Hall (QH) effect [1], the electrical characteristics of quantum Hall conductors (QHCs) have been intensely studied. The universal nature of the quantization in QHCs leads to a resistance that is independent of the microscopic properties of the sample. As a consequence, local properties of a QHC such as the current and voltage distributions within the sample are inaccessible with standard transport measurements. These local properties remain controversial, with some theories suggesting that the current flow and associated voltage drops are concentrated at the edges of the sample [2-5], while others predict a distribution extending throughout the bulk of the sample [6][7][8] The results, while informative, have lacked sufficient spatial and/or energy resolution to determine unambiguously how the current is partitioned between edge and bulk channels and the shape of the associated voltage profile across the QHC.To address these issues, we have used a scanned potential microscope to study the potential distribution in a QHC with submillivolt voltage and submicron spatial resolution. We find that at low magnetic fields the Hall voltage drop is linear, indicating uniform current flow throughout the sample. At high magnetic fields, large voltage drops are seen at the sample edges in the transition regions between QH plateaus, indicating that the current is concentrated near the edges. On the QH plateaus, the current is distributed throughout the bulk in a complex, non-uniform way. These results are in good agreement with existing results for edge and bulk transport in the QH regime.The samples consist of 10-20 µm wide Hall bars defined by wet etching of a GaAs/AlGaAs heterostructure with a 2D electron gas lying 77 nm beneath the surface. Results will be presented on two samples with mobilities of 8 and 70 m 2 /V-s and densities of 2.8 x 10 15 and 2.6 x 10 15 m -2 . All measurements were performed at temperatures between 0.7 and 1.0 K. The samples were also characterized by standard transport measurements.We measure the local voltage with a lowtemperature atomic force microscope (AFM) operating in non-contact mode [18]. As shown schematically in Fig. 1, an AC potential V 0 is applied to the contacts of the sample, producing inside the sample the AC potential V(x,y) whose spatial distribution is to be measured. The local sample potential V(x,y) interacts electrostatically with the sharp, metallized AFM tip, deflecting the AFM cantilever with a force that can be simply modelled...

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“…1,2 Since the discovery of the conductance quantization in these structures, 1 QPCs have been widely used in a variety of investigations, including transport through quantum dots, the quantum Hall effect, magnetic focusing, and the Aharonov-Bohm effect. 2 Also, with the rapid development on scanning probe microscope (SPM) techniques, it is possible to image current directly to study many remarkable phenomena, including quantum corrals, 3 electron flow through nanostructures, 4 charge distribution and photoactivity of dopant atoms, 5 and spectra of metallic nanoclusters. 6 Since the QPC plays such an important role in mesoscopic devices, it is an ideal system to be studied by the SPM techniques.…”

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confidence: 99%

Conductance of a quantum point contact in the presence of a scanning probe microscope tip

He¹,

Zhu

Wang

2002

Phys. Rev. B

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Using the recursive Green's function technique, we study the coherent electron conductance of a quantum point contact in the presence of a scanning probe microscope tip. Images of the coherent fringe inside a quantum point contact for different widths are obtained. It is found that the conductance of a specific channel is reduced while other channels are not affected as long as the tip is located at the positions correspending to that channel. Moreover, the coherent fringe is smoothed out by increasing the temperature or the voltage across the device. Our results are consistent with the experiments reported by Topinka et al. (Science 289, 2323(Science 289, (2000).PACS numbers: 73.23.-b, 73.43.Cd, 73.20.At (Phys. Rev. B 65, 205321 (2002)) Quantum point contacts (QPCs) formed in twodimensional electron gases (2DEGs) have attracted significant attention for the past two decades. 1,2 Since the discovery of the conductance quantization in these structures, 1 QPCs have been widely used in a variety of investigations, including transport through quantum dots, the quantum Hall effect, magnetic focusing, and the Aharonov-Bohm effect. 2

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Scanning Single-Electron Transistor Microscopy: Imaging Individual Charges

Cited by 284 publications

References 14 publications

Observation of electron–hole puddles in graphene using a scanning single-electron transistor

Observation of electron–hole puddles in graphene using a scanning single-electron transistor

Scanned potential microscopy of edge and bulk currents in the quantum Hall regime

Conductance of a quantum point contact in the presence of a scanning probe microscope tip

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