The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
The noncommutative geometry of the quantum Hall effect
Open accessAbstract
An overview of the integer quantum Hall effect is given. A mathematical framework using nonommutative geometry as defined by Connes is prepared. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.
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Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Electronic properties of two-dimensional systems
Ando, T., Fowler, A. B., & Stern, F. (1982) · Reviews of Modern Physics · doi:10.1103/revmodphys.54.437 · Cited by 7,455
Klitzing, K. V., Dorda, G., & Pepper, M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.494 · Cited by 7,119
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
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
Two-Dimensional Magnetotransport in the Extreme Quantum Limit
Tsui, D. C., Stormer, H. L., & Gossard, A. C. (1982) · Physical Review Letters · doi:10.1103/physrevlett.48.1559 · Cited by 4,788
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
Hofstadter, D. R. (1976) · Physical Review B · doi:10.1103/physrevb.14.2239 · Cited by 3,495
Halperin, B. I. (1982) · Physical Review B · doi:10.1103/physrevb.25.2185 · Cited by 2,547
Composite-fermion approach for the fractional quantum Hall effect
Jain, J. K. (1989) · Physical Review Letters · doi:10.1103/physrevlett.63.199 · Cited by 2,346
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
Haldane, F. D. M. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.605 · Cited by 2,210
Cited by
Anyons in an exactly solved model and beyond
Kitaev, A. (2006) · Annals of Physics · doi:10.1016/j.aop.2005.10.005 · Cited by 5,245
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Douglas, M., & Nekrasov, N. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.977 · Cited by 2,096
Topological insulators and superconductors: tenfold way and dimensional hierarchy
Ryu, S., Schnyder, A. P., Furusaki, A., & Ludwig, A. W. W. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/6/065010 · Cited by 2,045
Carr, S., Massatt, D., Fang, S., Cazeaux, P., Luskin, M., & Kaxiras, E. (2017) · Physical Review B · doi:10.1103/physrevb.95.075420 · Cited by 526
Metadata
- Authors
- Bellissard, J., van Elst, A., & Schulz- Baldes, H.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1994-10-01
- Volume
- 35
- Issue
- 10
- Pages
- 5373-5451
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1989661400
- Cited by
- 583
- References
- 49
- FWCI
- 8.34
- Type
- journal article
- Language
- en
- Open access
- green
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- Bellissard, J., van Elst, A., & Schulz- Baldes, H. (1994). The noncommutative geometry of the quantum Hall effect. Journal of Mathematical Physics. https://doi.org/10.1063/1.530758
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.
