Inter-edge-state scattering and nonlinear effects in a two-dimensional electron gas at high magnetic fields

Komiyama, S.; Hirai, Hiroshi; Ohsawa, Maki; Matsuda, Y.; Sasa, Shigehiko; Fujii, Toshio

doi:10.1103/physrevb.45.11085

Cited by 137 publications

(111 citation statements)

References 45 publications

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“…Impurities provide magnetic field gradients in the reference frame of the moving electrons, which can induce scattering between edge channels of opposite spin. Measurements of the equilibration length over macroscopic distances [5,6] are in agreement with the values obtained from the theory of this spin-orbit coupling mechanism [7][8][9][10][11]. Other possible mechanisms for inter-edge state coupling, for example magnetic impurities, are thought to play only a secondary role in clean Ga[Al]As heterostructures.…”

supporting

confidence: 85%

Individual scatterers as microscopic origin of equilibration between spin-polarized edge channels in the quantum Hall regime

Heinzel

Acremann

Ensslin

et al. 2000

Physica E: Low-dimensional Systems and Nanostructures

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The equilibration length between spin-polarized edge states in the Quantum Hall regime is measured as a function of a gate voltage applied to an electrode on top of the edge channels. Reproducible fluctuations in the coupling are observed and interpreted as a mesoscopic fingerprint of single spin-flip scatterers which are turned on and off. A model to analyze macroscopic edge state coupling in terms of individual scatterers is developed, and characteristic values for these scatterers in our samples are extracted. For all samples investigated, the distance between spin-flip scatterers lies between the Drude and the quantum scattering length.The unique transport properties of two-dimensional electron gases in the integer Quantum Hall regime [1] can, to a large extent, be explained in a single particle picture by electronic transport via edge channels [2], which carry the current without dissipation over macroscopic distances. The Quantum Hall effect is not influenced by scattering between edge channels running at the same side of the sample. Such scattering, however, does occur and can be detected in various ways, for example by measuring the equilibration between edge channels [3]. In a macroscopic picture, the equilibration between two edge channels can be described by the coupling P , a macroscopic quantity defined by P = (∆µ − ∆µ ′ )/∆µ, where ∆µ and ∆µ ′ are the differences in the electrochemical potential between the edge channels before and after the equilibration along a length L. The equilibration length ℓ eq is then defined by the length over which ∆µ is reduced to 1/e of its initial value, i.e.This picture does not contain information on the microscopic origin of edge state equilibration. However, it is generally accepted that equilibration between spinpolarized edge channels, separated in energy by gµ B B (g is the effective electronic g-factor, µ B the Bohr magneton, and B the magnetic field) takes place via spin-orbit coupling [3], in contrast to the equilibration between edge channels separated in energy by the Landau gap [4]. Impurities provide magnetic field gradients in the reference frame of the moving electrons, which can induce scattering between edge channels of opposite spin. Measurements of the equilibration length over macroscopic distances [5,6] are in agreement with the values obtained from the theory of this spin-orbit coupling mechanism [7][8][9][10][11]. Other possible mechanisms for inter-edge state coupling, for example magnetic impurities, are thought to play only a secondary role in clean Ga[Al]As heterostructures. In a recent work, Polyakov [12] argues that since these spin-flip transitions involve a momentum transfer to the impurity potential, their rate must be suppressed when the disorder is smooth. He concludes that the spinflip scattering is not only very sensitive to the local potential, but also that transitions are induced by rather rare fluctuations which provide a strong scattering potential. It is precisely this picture that we can support by the measurements presented...

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supporting

confidence: 85%

Individual scatterers as microscopic origin of equilibration between spin-polarized edge channels in the quantum Hall regime

Heinzel

Acremann

Ensslin

et al. 2000

Physica E: Low-dimensional Systems and Nanostructures

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“…Using submicron gates deposited on top of the heterostructure, however, one can selectively backscatter the edge states, induce different potentials in different edge states, and measure the resultant inter-edge scattering [13]. Scattering between spin-degenerate [14] and spin-split [15] edge states has been considered previously for the linear regime, as has non-linear scattering between spin-degenerate edge states [10,16]. In this paper, we report measurements of nonlinear transport between spin-split edge states, and show that spin-flip relaxation produces a nuclear polarization of the Ga and As nuclei.…”

Section: Introductionmentioning

confidence: 99%

Dynamic nuclear polarization at the edge of a two-dimensional electron gas

et al. 1997

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We have used gated GaAs/AlGaAs heterostructures to explore nonlinear transport between spin-resolved Landau level (LL) edge states over a submicron region of two-dimensional electron gas (2DEG). The current I flowing from one edge state to the other as a function of the voltage V between them shows diode-like behavior-a rapid increase in I above a well-defined threshold Vt under forward bias, and a slower increase in I under reverse bias. In these measurements, a pronounced influence of a current-induced nuclear spin polarization on the spin splitting is observed, and supported by a series of NMR experiments. We conclude that the hyperfine interaction plays an important role in determining the electronic properties at the edge of a 2DEG.

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“…The steps in conductance arise as the new modes pop through the Fermi surface one at a time so long as their separation exceeds kBT. Experiments in weak [13,14] and strong [15] magnetic fields obtained very non-classical behavior as well in the magnetoresistance, which has been attributed to extraordinary momentum conservation lengths [16]. As the magnetic field B increases and ħωc » 1 (where ω = eB/m is the cyclotron frequency), the transport crosses over to a "globally adiabatic" regime [17] where the momentum conservation length is many millimeters [18].…”

mentioning

confidence: 99%

“…The same kind of experiments can be performed at high magnetic field, where ħωc « 1 a n d t h e t r a n s p o r t i s d o m i n a t e d b y e d g e s t a t e s t h a t m a i n t a i n t h e i r momentum for macroscopic distances [16]. The high field magnetoconductance of several ballistic conductors has pointed toward even greater opportunity to make predictable interferometers -at least in an open geometry [15].…”

mentioning

confidence: 99%

Solid State Quantum Interferometers (with and without the Warts)

Washburn

1995

Acta Phys. Pol. A

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A brief review of quantum interference in small conductors is followed by a discussion of quantum interference in ballistic conductors. The ballistic conductors are characterized by conservation of the momentum vector and this leads to a simple model for the details of the conductance of the system. In contrast, for diffusive conductors one can only predict the statistical behavior of the interference contributions to the conductance. The response of the ballistic interferometers is governed by semiclassical physics of the electron momentum states (i.e. the modes) in the quantum conductor. Under circumstances of reduced backscattering of the modes, the interference pattern appears to imitate that from a simple optical interferometer. New results from ballistic interferometers are reviewed briefly.PACS numbers: 73.20.DxThe advent some years ago of quantum interference experiments led to a small revolution in the understanding of transport of electrons in the solid state [1]. First [2] in samples of size L much greater than the quantum coherence length Lô f the carriers and later [3] in samples of size L L, quantum interference was shown to be a significant perturbation on the average (classical) conductance. The quantum corrections to the average conductance arise through the interference of coherently propagating carriers, which contribution was ignored in the calculations of the average (Dude) conductance. Carrier excitations from the Fermi sea propagate for some distance and are scattered elastically by static impurities (lattice defects) along the way. The probability for a carrier to propagate from a certain point to another is given by the usual sum over all Feynman paths W = | Σn Qn |2 where Qn is a complex amplitude to propagate along the n-th trajectory between the two points. The total conductance of a conductor with two ports is G = (e2 /h) Σm Wm, where Wm is the transmission probability for the m-th mode in the conductor. The excitations are annihilated by inelastic scattering from dynamic excitations such as other carriers, phonons, spins, etc. [1]. At low

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Inter-edge-state scattering and nonlinear effects in a two-dimensional electron gas at high magnetic fields

Cited by 137 publications

References 45 publications

Individual scatterers as microscopic origin of equilibration between spin-polarized edge channels in the quantum Hall regime

Individual scatterers as microscopic origin of equilibration between spin-polarized edge channels in the quantum Hall regime

Dynamic nuclear polarization at the edge of a two-dimensional electron gas

Solid State Quantum Interferometers (with and without the Warts)

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