Interior contacts in a narrow quantum Hall bar: a two-dimensional self-consistent screening calculation of the current distribution
Abstract
We present fully two-dimensional self-consistent calculations of the electron density, local filling factor and current distribution in a six-terminal GaAs/AlGaAs Hall bar of width W = 3 micrometers with two additional square contacts, A and B, placed on the channel axis and connected to the outside by air bridges, following the interior-contact experiment of Kendirlik et al. [Nat. Commun. 8, 14082 (2017)]. Within the screening theory of the integer quantized Hall effect, the Thomas-Fermi-Poisson equations are solved on the full device plane, including the probe arms and the depletion regions around the interior contacts, and the current is obtained from a local Ohm's law with a filling-factor dependent conductivity tensor, for source-drain and interior-contact excitation separately. Across the nu = 2 plateau the interior contacts pass through three regimes as the field is lowered: galvanically connected to the current path in a compressible bulk, floating in the Hall potential of a fully incompressible bulk, and isolated from both the bulk and the edge strips by closed incompressible rings encircling each contact. In the floating and isolated regimes the two-terminal resistance between the interior contacts rises by orders of magnitude. The isolation interval lies within the Hall plateau and ends before its low-field edge; its high-field end is sharply set by the disappearance of the incompressible bulk, while its low-field end shrinks with temperature and Landau-level broadening. The resistance between an interior contact and a perimeter probe approaches one half of the quantized Hall resistance across the plateau. The topology of the incompressible regions and the boundaries of the isolation interval are insensitive to the regularization of the local conductivity, to the grid and to moderate disorder, whereas the magnitude of the isolation resistance is not.
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BibTeX
@misc{siddiki2026interior,
title = {{Interior contacts in a narrow quantum Hall bar: a two-dimensional self-consistent screening calculation of the current distribution}},
author = {A. Siddiki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00326},
eprint = {2610.00326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00326},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interior contacts in a narrow quantum Hall bar: a two-dimensional self-consistent screening calculation of the current distribution
AU - A. Siddiki
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00326
UR - https://arxiv.org/abs/2610.00326
AB - We present fully two-dimensional self-consistent calculations of the electron density, local filling factor and current distribution in a six-terminal GaAs/AlGaAs Hall bar of width W = 3 micrometers with two additional square contacts, A and B, placed on the channel axis and connected to the outside by air bridges, following the interior-contact experiment of Kendirlik et al. [Nat. Commun. 8, 14082 (2017)]. Within the screening theory of the integer quantized Hall effect, the Thomas-Fermi-Poisson equations are solved on the full device plane, including the probe arms and the depletion regions around the interior contacts, and the current is obtained from a local Ohm's law with a filling-factor dependent conductivity tensor, for source-drain and interior-contact excitation separately. Across the nu = 2 plateau the interior contacts pass through three regimes as the field is lowered: galvanically connected to the current path in a compressible bulk, floating in the Hall potential of a fully incompressible bulk, and isolated from both the bulk and the edge strips by closed incompressible rings encircling each contact. In the floating and isolated regimes the two-terminal resistance between the interior contacts rises by orders of magnitude. The isolation interval lies within the Hall plateau and ends before its low-field edge; its high-field end is sharply set by the disappearance of the incompressible bulk, while its low-field end shrinks with temperature and Landau-level broadening. The resistance between an interior contact and a perimeter probe approaches one half of the quantized Hall resistance across the plateau. The topology of the incompressible regions and the boundaries of the isolation interval are insensitive to the regularization of the local conductivity, to the grid and to moderate disorder, whereas the magnitude of the isolation resistance is not.
ER -