Self-consistent calculation of electric potentials in Hall devices

Kramer, Tobias; Krueckl, Viktor; Heller, Eric J.; Parrott, Robert E.

doi:10.1103/physrevb.81.205306

Cited by 19 publications

(25 citation statements)

References 22 publications

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“…This calculation scheme also presents the formation of compressible/incompressible strips in front of the contact. These non-ideal contact ideas are further supported by other recent theoretical investigations considering contacts [58,59].…”

Section: Two Edge Regimes At Four Characteristic B Fields With Idealsupporting

confidence: 77%

The visibility of IQHE at sharp edges: experimental proposals based on interactions and edge electrostatics

et al. 2012

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The influence of the incompressible strips on the integer quantized Hall effect (IQHE) is investigated, considering a cleaved-edge overgrown (CEO) sample as an experimentally realizable sharp edge system. We propose a set of experiments to clarify the distinction between the large-sample limit when bulk disorder defines the IQHE plateau width and the small-sample limit smaller than the disorder correlation length, when self-consistent edge electrostatics define the IQHE plateau width. The large-sample or bulk quantized Hall (QH) regime is described by the usual localization picture, whereas the small-sample or edge regime is discussed within the compressible/incompressible strips picture, known as the screening theory of QH edges. Utilizing the unusually sharp edge profiles of the CEO samples, a Hall bar design is proposed to manipulate the edge potential profile from smooth to extremely sharp. By making use of a sidegate perpendicular to the two-dimensional electron system, it is shown that the plateau widths can be changed or even eliminated altogether. Hence, the visibility of IQHE is strongly influenced when adjusting the edge potential profile and/or changing the dc current direction under high currents in the nonlinear transport regime. As a second investigation, we consider two different types of ohmic 4 2 contacts, namely highly transmitting (ideal) and highly reflecting (non-ideal) contacts. We show that if the injection contacts are non-ideal, but still ohmic, it is possible to measure directly the non-quantized transport taking place at the bulk of the CEO samples. The results of the experiments we propose will clarify the influence of the edge potential profile and the quality of the contacts, under QH conditions. Contents

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Section: Two Edge Regimes At Four Characteristic B Fields With Idealsupporting

confidence: 77%

The visibility of IQHE at sharp edges: experimental proposals based on interactions and edge electrostatics

et al. 2012

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“…[10][11][12] For the determination of the classical Hall potential, the metallic contacts have to be considered as equipotential surfaces, which enforce also in the two-dimensional subsystem a uniform potential underneath the contacts. 13 The two-terminal resistance of a classical Hall device can be readily calculated by the ratio of the source-drain voltage to the source-drain current. The specific device geometry and the placement of metallic contacts do have a strong influence on the Hall potential solution.…”

mentioning

confidence: 99%

“…The specific device geometry and the placement of metallic contacts do have a strong influence on the Hall potential solution. 13 The fundamental reason for the formation of the Hall potential is the interactions between the electrons in the complete device, including the contacts, which transform the magnetic Lorentz force acting on every electron into a global, nontrivial adjustment of the potential with the emergence of two hot spots at opposite corners of the device. The interactions are not present in a Fermi-liquid model of effectively noninteracting electrons, 8 and thus these models are not sufficient to explain the experimental observations of hot spots and the emergence of the classical Hall field in the QHE.…”

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confidence: 99%

“…In the following, we will use the uniform-map solution as the mean-field potential, which emerges due to interaction and screening between the electrons and the positive charges and by considering the metallic boundary conditions at source and drain. 13 We study the propagation of the effectively noninteracting electrons in the mean-field potential. We view our model as providing a starting point for a more rigorous inclusion of interaction effects, already in the nonfractional QHE.…”

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confidence: 99%

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Theory of the quantum Hall effect in finite graphene devices

et al. 2010

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We study the quantum Hall effect ͑QHE͒ in graphene based on the current injection model, which takes into account the finite rectangular geometry with source and drain electrodes. In our model, the presence of disorder, the edge-state picture, extended states, and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.

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“…With the discovery of the fractional Quantum Hall effect (FQHE) in systems of interacting electrons in quasi two-dimensional systems, many theoretical approaches for studying interacting electrons have been proposed, including the celebrated Laughlin wave-function for electrons in the lowest Landau level. In the experimentally realized Hall devices translational symmetry is broken by the current source and drain contacts, which lead to the formation of hot-spots with high electric field values [21,22]. A comparison of the various theoretical approaches with numerical methods is often performed for few-electron quantum dots.…”

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confidence: 99%

Interacting electrons in a magnetic field in a center-of-mass free basis

Krämer¹,

Kramer²

2015

Phys. Scr.

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We present an extension of the spin-adapted configuration-interaction method for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and center-of-mass coordinates we obtain an analytical identification of all spurious center-of-mass states of the Coulomb-interacting electrons. We find a substantial reduction in the basis set used for numerical computations. At the same time we increase the accuracy compared to the standard spinadapted configuration-interaction method (SACI) due to the absence of distortions caused by an unbalanced cut-off of center-of-mass excitations.Dedicated to Margarita and Vladimir Man'ko on the occasion of their 150th birthday.

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Self-consistent calculation of electric potentials in Hall devices

Cited by 19 publications

References 22 publications

The visibility of IQHE at sharp edges: experimental proposals based on interactions and edge electrostatics

The visibility of IQHE at sharp edges: experimental proposals based on interactions and edge electrostatics

Theory of the quantum Hall effect in finite graphene devices

Interacting electrons in a magnetic field in a center-of-mass free basis

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