Scanning capacitance imaging of compressible and incompressible quantum Hall effect edge strips

Suddards, M.E.; Baumgärtner, A.; Henini, M.; Mellor, C.J.

doi:10.1088/1367-2630/14/8/083015

Cited by 46 publications

(46 citation statements)

References 31 publications

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“…Recent scanning probe microscopy experiments [20][21][22][23] have demonstrated the existence of these strips several magnetic lengths away from the edge. In the opposite limit, l s o ol B , the case of the experiments reported here, the strips are absent, and the Nth LL shifts monotonically away from the DP for distances within ffiffiffiffi N p l B of the edge [5][6][7] .…”

Section: Resultsmentioning

confidence: 99%

“…However, in the semiconductor-based 2DES studied thus far, this 'topologically protected' correspondence is notoriously difficult to realize 11,12 . The most likely cause of the discrepancy between theory and experiment is the generic occurrence of edge reconstruction [13][14][15][16][17][18][19][20][21][22][23] in the semiconductor 2DES, which induces additional edge modes that are not tied to the bulk topology and disrupt the predicted universality 24 . In these systems, the lithographically defined edges have soft confinement potentials, caused by the gates and dopant layer being far away from the 2DES, which favour the reconstruction of the edge states into alternating compressible and incompressible strips (Fig.…”

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confidence: 99%

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Evolution of Landau levels into edge states in graphene

Luican‐Mayer

Abanin

et al. 2013

Nat Commun

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Two-dimensional electron systems in the presence of a magnetic field support topologically ordered states, in which the coexistence of an insulating bulk with conducting one-dimensional chiral edge states gives rise to the quantum Hall effect. For systems confined by sharp boundaries, theory predicts a unique edge-bulk correspondence, which is central to proposals of quantum Hall-based topological qubits. However, in conventional semiconductor-based two-dimensional electron systems, these elegant concepts are difficult to realize, because edge-state reconstruction due to soft boundaries destroys the edge-bulk correspondence. Here we use scanning tunnelling microscopy and spectroscopy to follow the spatial evolution of electronic (Landau) levels towards an edge of graphene supported above a graphite substrate. We observe no edge-state reconstruction, in agreement with calculations based on an atomically sharp boundary. Our results single out graphene as a system where the edge structure can be controlled and the edge-bulk correspondence is preserved.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Evolution of Landau levels into edge states in graphene

Luican‐Mayer

Abanin

et al. 2013

Nat Commun

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“…Their theoretically predicted existence has been investigated in various experiments including electrostatic transparency and dynamical scanning capacitance measurements2021. The theoretical prediction of the existence of compressible and incompressible strips dates back to 1990, propounded by Chang22.…”

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confidence: 99%

Anomalous resistance overshoot in the integer quantum Hall effect

Kendirlik

Sirt

Kalkan

et al. 2013

Sci Rep

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In this work we report on experiments performed on smooth edge-narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and even integer plateaus, which favor a spin independent explanation, in contrast to discussion in the literature. In a second set of the experiments, we investigate the overshoot effect in gate defined Hall bar and explicitly show that the amplitude of the overshoot effect can be directly controlled by gate voltages. We offer a comprehensive explanation based on scattering between evanescent incompressible channels.T he overwhelming interest to utilize quantum mechanics in applied technologies finds one of its first manifestations in the integer quantized Hall effect (IQHE) 1 . The magnetic field dependence of the transport coefficients of a two dimensional electron system (2DES) provides a possibility to standardize resistance in units of the von Klitzing constant h/e 2 , where h is the Planck constant and e is the elementary charge. However, an unexpected non-monotonic magnetic field dependence of the Hall resistance at the low-field-end of the quantized plateaus, known as the overshoot effect, remains a puzzle despite of both theoretical and experimental efforts in various material systems including GaAs/AlGaAs heterostructure 2-6 as well as Si/SiGe 7-13 and Si metal oxide semiconductor field effect transistors 14 . The utilization of the quantized Hall effect as a resistance standard is hindered by such anomalies, especially because their physical mechanism is not well understood. The overshoot effect is observed in these material systems at various filling factors n, defined by the number of occupied quantized (spin resolved) Landau levels (LL) below the Fermi energy. The effect has already been observed in the 1980's, where its physical mechanism was attributed to non-ideal contacts 2-4 , but without providing clear evidence for this hypothesis. Later, the overshoot effect was attributed to the decoupling of the spin-split states within the same LL at odd filling factors by Richter and Wheeler 5 , or, alternatively by the scattering between edge states together with spin-orbit interaction by Komiyama and Nii 6 . Recently, the overshoot effect has been investigated in Si/SiGe heterostructures as a function of current and temperature 12 . These experimental results have been elegantly explained within the screening theory of the integer quantized Hall effect, which explicitly takes into account the direct Coulomb interaction between charge carriers. In this approach the overshoot effect is described using co-existing (curr...

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“…SCM characterizes the surface of the sample by the change in the electrostatic capacitance between the surface and the probe and is a useful tool to reconstruct the surface topography of a rough metallic sample based on its capacitance image (dependence of capacitance of the system on a relative angular probe/sample position). Recent developments in the field are described, for example, in [3][4][5][6]. Various algorithms have been developed to allow efficient capacitance calculations [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Rigorous Approach to Calculation of Capacitance Images of Metallic Samples for Use in Capacitance Microscopy

Safonova¹,

Vinogradova²

2013

PIER B

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Abstract-A high-efficiency rigorous approach for the solution of the two-dimensional Laplace equation with Dirichlet's boundary conditions is developed to tackle electrostatic problems involving metallic cylinders of arbitrarily cross-sections. In this paper, we demonstrate how this novel algorithm can be used to address the problems arising in the capacitance microscopy to provide a higher resolution in studies of micro-cavities and whiskers on the surface of metallic samples. The precise capacitance images of the probe/sample systems are presented.

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Scanning capacitance imaging of compressible and incompressible quantum Hall effect edge strips

Cited by 46 publications

References 31 publications

Evolution of Landau levels into edge states in graphene

Evolution of Landau levels into edge states in graphene

Anomalous resistance overshoot in the integer quantum Hall effect

Rigorous Approach to Calculation of Capacitance Images of Metallic Samples for Use in Capacitance Microscopy

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