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Cited by 2,547Quantum and electron transport phenomenaTopological Materials and PhenomenaSurface and Thin Film Phenomena

Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential

Halperin, B. I.·1982·Physical Review B
DOI 10.1103/physrevb.25.2185
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Abstract

When a conducting layer is placed in a strong perpendicular magnetic field, there exist current-carrying electron states which are localized within approximately a cyclotron radius of the sample boundary but are extended around the perimeter of the sample. It is shown that these quasi-one-dimensional states remain extended and carry a current even in the presence of a moderate amount of disorder. The role of the edge states in the quantized Hall conductance is discussed in the context of the general explanation of Laughlin. An extension of Laughlin's analysis is also used to investigate the existence of extended states in a weakly disordered two-dimensional system, when a strong magnetic field is present.

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Crossref · 10.1103/physrevb.25.2185

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7 of 7 references verified0 citation errors · 0 not checkable

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  • TRS causes localization in 2D, and has to be broken to allow for current-carrying extended states.

    “The reason is that TRS causes localization in 2D, and has to be broken to allow for the existence of current-carrying extended states [19].”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [19]

  • Some extended states will survive as long as the disorder is not strong enough to disrupt the Landau level picture.

    “As argued in [19], some extended states will survive, as long as the disorder is not strong enough to disrupt the Landau level picture.”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [19]

  • Upward curving of Landau levels near the edges leads to net azimuthal currents.

    “Furthermore, the upward curving of the Landau levels near the edges leads to the appearance of net azimuthal currents [17,19].”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [19]

  • The occupation of localized states does not affect Hall conductivity, which gives robustness to quantization (plateaus) in disordered systems.

    “Popunjenost lokaliziranih stanja ne utjeˇ ce na Hallovu vodljivost, što daje robusnost kvantizaciji (pojava platoa) kod sustava s neredom kod kojih lokalizirana stanja obiˇ cno zauzimaju širi spektar energija unutar vrpce od protežnih stanja koja se nalaze po sredini vrpce [17,19].”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [19]

  • When a system is confined to an annulus between two radii and magnetic flux through the hole is adiabatically increased, spectral flow occurs.

    “Kad sustav ograniˇ cimo na prsten izme ¯ du dva radijusa te adijabatski pove´ cavamo magnetski tok kroz šupljinu prstena, uoˇ cavamo pojavu spektralnog toka [17,19].”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [19]

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Authors
Halperin, B. I.
Affiliations
Harvard University (US)
Corresponding author
Halperin, B. I.
ORCID
Halperin, B. I.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1982-02-15
Volume
25
Issue
4
Pages
2185-2190
ISSN
0163-1829 (ISSN-L)
DOI
10.1103/physrevb.25.2185
OpenAlex
W2121123255
Cited by
2,547
References
7
Citations by year
2026: 43 · 2025: 86 · 2024: 104 · 2023: 82 · 2022: 91 · 2021: 103 · 2020: 155 · 2019: 85 · 2018: 72 · 2017: 99 · 2016: 81 · 2015: 64 · 2014: 74 · 2013: 88 · 2012: 76
FWCI
26.35
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical review. B, Condensed matter (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Surface and Thin Film Phenomena
Keywords
Hall conductance quantization, edge states, extended states, two-dimensional disordered systems, high magnetic fields, disorder, cyclotron radius

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