The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Localization, percolation, and the quantum Hall effect
Abstract
Noninteracting electrons in a smooth two-dimensional random potential are localized in the large magnetic field limit. In contrast to Anderson localization, eigenstates with large localization lengths occur with a probability proportional to a universal power of their size, with the power given in terms of percolation critical exponents. Adding a parallel electric field $\stackrel{\ensuremath{\rightarrow}}{\mathcal{E}}$ causes extended states to appear in numbers proportional to a power of $\mathcal{E}$. This implies a nonlinear broadening of steps in the quantized Hall conductivity. The results for a parallel electric field are obtained by considering a graded percolation problem, in which the probability that a site is occupied varies with position.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Klitzing, K. V., Dorda, G., & Pepper, M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.494 · Cited by 7,119
Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
Abrahams, E., Anderson, P. W., Licciardello, D. C., & Ramakrishnan, T. V. (1979) · Physical Review Letters · doi:10.1103/physrevlett.42.673 · Cited by 6,134
Halperin, B. I. (1982) · Physical Review B · doi:10.1103/physrevb.25.2185 · Cited by 2,547
Scaling theory of percolation clusters
Stauffer, D. (1979) · Physics Reports · doi:10.1016/0370-1573(79)90060-7 · Cited by 2,365
Quantized Hall conductivity in two dimensions
Laughlin, R. B. (1981) · Physical Review B · doi:10.1103/physrevb.23.5632 · Cited by 2,162
Essam, J. W. (1980) · Reports on Progress in Physics · doi:10.1088/0034-4885/43/7/001 · Cited by 1,018
Aoki, H., & Ando, T. (1981) · Solid State Communications · doi:10.1016/0038-1098(81)90021-1 · Cited by 360
Quantized Hall effect at low temperatures
Paalanen, M. A., Tsui, D. C., & Gossard, A. C. (1982) · Physical Review B · doi:10.1103/physrevb.25.5566 · Cited by 166
Quantum percolation and quantization of Hall resistance in two-dimensional electron gas
Kazarinov, R. F., & Luryi, S. (1982) · Physical review. B, Condensed matter · doi:10.1103/physrevb.25.7626 · Cited by 154
Localisation and the two-dimensional Hall effect
Thouless, D. J. (1981) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/14/23/022 · Cited by 99
Cited by
Localization: theory and experiment
Kramer, B., & MacKinnon, A. (1993) · Reports on Progress in Physics · doi:10.1088/0034-4885/56/12/001 · Cited by 1,926
Sahimi, M. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.1393 · Cited by 1,082
Topological orders and edge excitations in fractional quantum Hall states
Wen, X.-G. (1995) · Advances in Physics · doi:10.1080/00018739500101566 · Cited by 1,060
von Klitzing, K. (1986) · Reviews of Modern Physics · doi:10.1103/revmodphys.58.519 · Cited by 800
Integer quantum Hall transition: An alternative approach and exact results
Ludwig, A. W. W., Fisher, M. P. A., Shankar, R., & Grinstein, G. (1994) · Physical Review B · doi:10.1103/physrevb.50.7526 · Cited by 709
Metadata
- Authors
- Trugman, S. A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1983-06-15
- Volume
- 27
- Issue
- 12
- Pages
- 7539-7546
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W1978085996
- Cited by
- 364
- References
- 14
- FWCI
- 7.40
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Localization, percolation, and the quantum Hall effect. https://app.cochat.ai/papers/10.1103/physrevb.27.7539
- The paper
- Trugman, S. A. (1983). Localization, percolation, and the quantum Hall effect. Physical Review B. https://doi.org/10.1103/physrevb.27.7539
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
