Origin of Landau oscillations observed in scanning tunneling spectroscopy on<b><i>n</i></b>-InAs(110)

Morgenstern, Markus; Haude, D.; Guðmundsson, Viðar; Wittneven, Chr.; Dombrowski, R.; Wiesendanger, R.

doi:10.1103/physrevb.62.7257

Cited by 31 publications

(15 citation statements)

References 21 publications

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“…Note that the lowest LL peak energy depends on the actual filling factor. The fact that the peaks are observable in the presence and the absence of the QD peak reveals that they are caused by the 2DES [16]. Interestingly, the peak widths are smaller in the second subband, which is in accordance with the known decreasing influence of the disorder on higher subbands [17].…”

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confidence: 78%

Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields

et al. 2003

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The local density of states of the adsorbate-induced two-dimensional electron system is studied in magnetic fields up to B=6 T. Landau quantization is observed and drift states with a width of about the magnetic length are found in agreement with theoretical predictions. At the tails of the Landau levels the states form closed paths indicating localization. These states show the expected energy dependence. A multifractal analysis applied to the data results in a nice parabolic shape of the characteristic f(alpha) spectra, but we find only a slight displacement of the origin from alpha=2.0 for the states in the center of the Landau level.

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confidence: 78%

Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields

et al. 2003

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“…With a coherence length coh ϭ100 nm estimated from the visible length scale of scattering states around individual dopants 17,21 as the depth up to which states contribute to the tunneling current, and with a calculated finite lifetime broadened DOS D(E) of the system at Bϭ6 T, 22 we obtain NӍD(E)⌬E coh Aϭ25 states on an area Aϭ200ϫ200 nm 2 , i.e., an average area per contributing state of about A n Ӎ40ϫ40 nm 2 .…”

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confidence: 99%

“…23 In magnetic field, these states are classified by three quantum numbers: the Landau level number n, the orbital momentum m, and the spin s. On previous measurements we found that only the mϭ0 states, which have a lateral diameter ͓full width at half maximum ͑FWHM͔͒ of the magnetic length (l b ϭ10 nm at 6 T͒ can significantly couple to the tunneling current. 22 Consequently, the averaged dI/dV curves are dominated by (mϭ0) states exhibiting Landau and spin levels of the QD. Often, the spin levels are not visible due to inherent broadening effects.…”

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confidence: 99%

Experimental evidence for edge-like states in three-dimensional electron systems

et al. 2001

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The local density of states ͑DOS͒ of n-InAs͑110͒ is measured in the extreme quantum limit by lowtemperature scanning tunneling microscopy. Based on the general trends published previously ͓Phys. Rev. Lett. 86, 1582 ͑2001͔͒ we analyze the data in more detail. First the influence of the tip induced quantum dot is studied. It turns out that the observed serpentine structures are not correlated with the properties of the quantum dot, which lead us to the conclusion that they are caused by the three-dimensional ͑3D͒ DOS of the semiconductor. The serpentine structures move with increasing energy similar to equipotential lines of a twodimensional potential landscape. With increasing magnetic field additional serpentines appear until a complete network penetrates the visible area. Moreover, an uncorrugated DOS coexists with the serpentine structures up to the highest magnetic field of 6 T. The results lead us to the conclusion that an increasing part of the DOS is localized in the direction parallel to the magnetic field, effectively acting as a two-dimensional DOS and thus exhibiting edgelike states. This implies that the steplike feature of the Hall resistance in the extreme quantum limit is a precursor of a quantized Hall step.

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“…This is not surprising, since the states probed by STS have their main weight in the inner 20 nm of the QD. 3 Thus the surface potential acts as a local perturbation on the QD states. Of course, potential fluctuations on a smaller length scale than the extension of the states, which exist close to individual dopants, are averaged out.…”

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“…The spin splitting results partly from the large g factor of bulk InAs caused by spin-orbit interaction and leading to a uniform spin splitting of 5 meV at Bϭ6 T. The additionally enhanced and fluctuating spin splitting of the QD is due to the exchange interaction as evidenced by Hartree-Fock calculations of the QD, performed with different configurations of an impurity, which are able to reproduce the experimentally observed additional g-enhancement. 3 Since the exchange interaction mixes all pairs of QD states and thus depends in a nonlocal way on the surface potential, it naturally explains the differences in shape between the spin splitting maps and the surface potential map. In turn, the measured spin splitting maps compared with the surface potential map represent, to our knowledge, the first microscopic visualization of the nonlocal character of the exchange interaction.…”

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Nonlocality of the exchange interaction probed by scanning tunneling spectroscopy

et al. 2001

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The energy states of the tip induced quantum dot are investigated in a magnetic field as a function of the tip position with respect to the surface. To study the influence of potential perturbations on the exchange interaction in the quantum dot, emphasis is given on the Landau and spin levels probed at positive bias. Mapping of the spatial dependence of the peak energies and comparison with the surface potential map-reconstructed from the analysis of scattering states around ionized dopants-reveals that the fluctuating surface potential acts as a local perturbation on the quantum dot states. In contrast, the spin splitting is influenced nonlocally by the surface potential, which directly evidences the nonlocal character of the exchange interaction.Quantum dots, often called artificial atoms, have been investigated extensively in the past, since their increased size with respect to atoms allows to study the influence of strong magnetic fields and correlation effects on the electronic structure of a system confined in all three dimensions. 1 The small electron density in the quantum dot favors the influence of electron-electron interactions. In particular, the nonlocal character of the exchange interaction leads to a complex correlation of the energy levels with potential perturbations always present in real systems.The aim of this Rapid Communication is to probe these correlations. We use the recently discovered tip induced quantum dot ͑QD͒, 2 introduced into a semiconductor surface by the tip of a scanning tunneling microscope ͑STM͒. The tip acts as a local gate movable over the surface and, by moving the QD probes different potential environments of the surface. Thus the potential fluctuations of the sample act as spatially varying perturbations on the confinement potential. The resulting exchange interaction is directly probed by measuring the spin splitting of the QD, i.e., we record dI/dV curves exhibiting spin split states in magnetic field. 3 A comparison of the resulting spatial map of the spin splitting with the surface potential map answers the question, if the exchange interaction reacts locally or nonlocally on potential perturbations. As expected, we find a nonlocal correlation, which, to our knowledge, is the first microscopic visualization of the nonlocal character of the exchange interaction.Besides this physical aspect, the study has also a technological aspect: the spin of a quantum dot has been proposed as a basic unit ͑qubit͒ in quantum computation. 4 The spin degree of freedom provides a reasonable coherence time and, importantly, the approach can be extended to a large number of qubits. 5 However, in contrast to atoms, quantum dots suffer from their imperfections in the confinement potential leading to slightly varying level schemes between nominally identical dots. 6 Hence, the influence of potential perturbations on the spin splitting has to be understood to realize controllable devices. This study is a first step in that direction, although we did not find a quantitative model to explain...

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Origin of Landau oscillations observed in scanning tunneling spectroscopy onn-InAs(110)

Cited by 31 publications

References 21 publications

Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields

Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields

Experimental evidence for edge-like states in three-dimensional electron systems

Nonlocality of the exchange interaction probed by scanning tunneling spectroscopy

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