Subband Structure of Quantum Wires in Magnetic Fields

Suzuki, Tatsuo; Ando, Tsuneya

doi:10.1143/jpsj.62.2986

Cited by 72 publications

(64 citation statements)

References 20 publications

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“…The situation is consistent with the single antidot experiment by Karakurt et al [9], who argued that the perfectly compressible regions are not formed around an antidot. This is also in qualitative agreement with the calculations of the edge states in quantum wires [18,19]. Suzuki and Ando [18] demonstrated in a self-consistent Hartree approximation that the complete flattening of the compressible stripes does not appear in a narrow wire with width 100-200 nm.…”

supporting

confidence: 87%

“…This is also in qualitative agreement with the calculations of the edge states in quantum wires [18,19]. Suzuki and Ando [18] demonstrated in a self-consistent Hartree approximation that the complete flattening of the compressible stripes does not appear in a narrow wire with width 100-200 nm. As mentioned before, our sample can be regarded as a network of the wire with the width $100 nm.…”

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confidence: 87%

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Temperature-Dependent Screening of the Edge State around Antidots in the Quantum Hall Regime

et al. 2009

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The Aharonov-Bohm effect in a small array of antidots with a large aspect ratio is investigated in the quantum Hall regime. The evolution with temperature of the Aharonov-Bohm oscillations in the magnetic field versus gate voltage (B-V_{g}) plane reveals the temperature dependence of the screening. The self-consistently screened potential of the compressible band surrounding an antidot is observed to gain a progressively steeper slope with increasing temperature.

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confidence: 87%

supporting

confidence: 87%

Temperature-Dependent Screening of the Edge State around Antidots in the Quantum Hall Regime

et al. 2009

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“…This leads to a metallic behavior when the electron density is redistributed (compressed) to keep the electrostatic potential constant. In the incompressible regions, where the Fermi energy lies in the Landau gaps, all the levels below E F are completely filled and hence the electron density is constant (which is consistent with the behavior of the incompressible liquid).A number of studies addressing the problem of electron-electron interaction in quantum wires beyond the electrostatic treatment of the edge states of Chklovskii et al2 have been reported during the recent decade 3,4,5,6,7,8,9,10,11,12,13,14 . The many-body aspects of the problem have been included within ThomasFermi 3 , Hartree-Fock 4,5,6 , screened Hartree-Fock 7 , and the density functional theory 8,9 .…”

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confidence: 59%

Spin polarization of edge states and the magnetosubband structure in quantum wires

2006

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We provide a quantitative description of the structure of edge states in split-gate quantum wires in the integer quantum Hall regime. We develop an effective numerical approach based on the Green's function technique for the self-consistent solution of Schrödinger equation where electron-and spin interactions are included within the density functional theory in the local spin density approximation. The major advantage of this technique is that it can be directly incorporated into magnetotransport calculations, because it provides the self-consistent eigenstates and wave vectors at a given energy, not at a given wavevector (as conventional methods do). We use the developed method to calculate the subband structure and propagating states in the quantum wires in perpendicular magnetic field starting with a geometrical layout of the wire. We discuss how the spin-resolved subband structure, the current densities, the confining potentials, as well as the spin polarization of the electron and current densities evolve when an applied magnetic field varies. We demonstrate that the exchange and correlation interactions dramatically affect the magnetosubbands in quantum wires bringing qualitatively new features in comparison to a widely used model of spinless electrons in Hartree approximation. I. INRODUCTIONTransport properties of quantum dots, antidots and related structures are affected by the nature of currentcarrying states in the leads connecting these structures to electron reservoirs. In sufficiently high magnetic fields the current-carrying states are the edge states propagating in a close vicinity to the sample boundaries 1 . A detailed information on the structure of the edge states represent a key to the understanding of various features of the magnetotransport in the quantum Hall regime.A quantitative description of the edge states for the case of the gate-induced confinement of the highmobility two-dimensional electron gas (2DEG) was given by Chklovskii et al.2 , who provided an analytical solution for the positions and widths of the compressible and incompressible strips arising in the 2DEG due to the electrostatic screening. In the compressible regions, the Landau bands are pinned at the Fermi energy E F . This leads to a metallic behavior when the electron density is redistributed (compressed) to keep the electrostatic potential constant. In the incompressible regions, where the Fermi energy lies in the Landau gaps, all the levels below E F are completely filled and hence the electron density is constant (which is consistent with the behavior of the incompressible liquid).A number of studies addressing the problem of electron-electron interaction in quantum wires beyond the electrostatic treatment of the edge states of Chklovskii et al.2 have been reported during the recent decade 3,4,5,6,7,8,9,10,11,12,13,14 . The many-body aspects of the problem have been included within ThomasFermi 3 , Hartree-Fock 4,5,6 , screened Hartree-Fock 7 , and the density functional theory 8,9 . The full quantummechanical calc...

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“…However, once the strip widths become comparable with the magnetic length the TFA is prone to fail23. At this point scattering across the strip becomes more probable2526. Furthermore, the electron density and compressibility are thermodynamic quantities which are only properly defined for length scales larger than the mean electron distance.…”

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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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Subband Structure of Quantum Wires in Magnetic Fields

Cited by 72 publications

References 20 publications

Temperature-Dependent Screening of the Edge State around Antidots in the Quantum Hall Regime

Temperature-Dependent Screening of the Edge State around Antidots in the Quantum Hall Regime

Spin polarization of edge states and the magnetosubband structure in quantum wires

Anomalous resistance overshoot in the integer quantum Hall effect

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