The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Open accessAbstract
The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential $U$. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small $\frac{U}{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}$.
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“These transitions can be regarded as a realization of the two-dimensional quantum Hall effect in zero net field discussed by Haldane. 10”
From Antiferromagnetic topological insulators (2010) · cites this paper as [10]
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In the citing paper
“The corresponding Lorentz-like force in reciprocal space provides an anomalous velocity term which is responsible, e.g., for the anomalous and integer (Thouless et al., 1982) quantum Hall effects.”
From Topological photonics (2019) · cites this paper as Thouless et al., 1982
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In the citing paper
“Topological consequences of Weyl nodes began to be explored with the realization that Berry curvature plays a key role in determining the Hall effect (Karplus and Luttinger, 1954; Thouless et al. , 1982), and the Weyl nodes are related to 'diabolic points' discussed by Berry as sources of Berry flux (Berry, 1985).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Thouless et al., 1982
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In the citing paper
“Soon after, the extremely robust quantization of the Hall conductance was related to the topology of bands in momentum space by Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) (Thouless et al., 1982).”
From Topological photonics (2019) · cites this paper as Thouless et al., 1982
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In the citing paper
“Within linear response theory and ignoring interparticle interactions, one can show that the Hall conductance σ xy of a two-dimensional insulator is (Thouless et al., 1982) σ xy ¼ - e 2 h X n C n”
From Topological photonics (2019) · cites this paper as Thouless et al., 1982
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“These works related the integer appearing in the Hall conductance to a topological invariant of the system, the Chern number, that is an integer-valued quantity which describes the global structure of the wave function in momentum space over the Brillouin zone.”
From Topological photonics (2019) · cites this paper as Thouless et al. (1982)
In the citing paper
“In a twodimensional (2D) quantum Hall system, for example, the integral of the Berry curvature over the 2D Brillouin zone determines the Chern number: a global topological invariant that underlies the quantization of Hall transport for a 2D filled energy band 2 .”
From Experimental measurement of the Berry curvature from anomalous transport (2017) · cites this paper as [2]
In the citing paper
“When a lattice is put in a commensurate magnetic field (one with rational flux per unit cell, in units of the flux quantum so that Bloch's theorem applies), each occupied band j contributes an integer (48)”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [48]
In the citing paper
“The sign of the Hall conductance depends on the sign of the effective Dirac mass, 10,31,32 which here is set by the direction of the Zeeman field at the surface.”
From Antiferromagnetic topological insulators (2010) · cites this paper as [10]
In the citing paper
“Note that the total conductance of a slab is always an integer, as required. 10,11,33”
From Antiferromagnetic topological insulators (2010) · cites this paper as [10]
In the citing paper
“In this geometry this coupling vanishes as the cross products d 1 × d 2 from the two paths cancel.”
From Antiferromagnetic topological insulators (2010) · cites this paper as [10]
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Citations
Cites
Klitzing, K. V., Dorda, G., & Pepper, M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.494 · Cited by 7,119
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
Quantized Hall conductivity in two dimensions
Laughlin, R. B. (1981) · Physical Review B · doi:10.1103/physrevb.23.5632 · Cited by 2,162
Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
Harper, P. G. (1955) · Proceedings of the Physical Society. Section A · doi:10.1088/0370-1298/68/10/304 · Cited by 1,416
Aoki, H., & Ando, T. (1981) · Solid State Communications · doi:10.1016/0038-1098(81)90021-1 · Cited by 360
Quantized Hall resistance and the measurement of the fine-structure constant
Prange, R. E. (1981) · Physical review. B, Condensed matter · doi:10.1103/physrevb.23.4802 · Cited by 336
A Result Not Dependent on Rationality for Bloch Electrons in a Magnetic Field
Wannier, G. H. (1978) · physica status solidi (b) · doi:10.1002/pssb.2220880243 · Cited by 241
Magnetic Translation Group. II. Irreducible Representations
Zak, J. (1964) · Physical Review · doi:10.1103/physrev.134.a1607 · Cited by 238
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 97
Self-citationBloch Electrons in Irrational Magnetic Fields
Rauh, A., Wannier, G. H., & Obermair, G. M. (1974) · physica status solidi (b) · doi:10.1002/pssb.2220630121 · Cited by 69
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Xiao, D., Shi, J., Clougherty, D. P., & Niu, Q. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.087602 · Cited by 65
Free-fermion entanglement spectrum through Wannier interpolation
Lee, C. H., & Ye, P. (2015) · Physical Review B · doi:10.1103/physrevb.91.085119 · Cited by 54
Dynamical Meaning of Quantum Adiabatic Phase: The Case of a Noncanonical System
Kuratsuji, H., & Iida, S. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.1003 · Cited by 41
Cserti, J., & Dávid, G. (2010) · Physical Review B · doi:10.1103/physrevb.82.201405 · Cited by 24
Creation and manipulation of anyons in a layered superconductor–two-dimensional electron gas system
Rosenberg, G., Seradjeh, B., Weeks, C., & Franz, M. (2009) · Physical Review B · doi:10.1103/physrevb.79.205102 · Cited by 19
Liu, X., Wang, Z., Xie, X. C., & Yu, Y. (2011) · Physical Review B · doi:10.1103/physrevb.83.125105 · Cited by 13
Weyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv
Metadata
- Authors
- Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M.
- Affiliations
- University of Washington (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1982-08-09
- Volume
- 49
- Issue
- 6
- Pages
- 405-408
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2037807652
- Cited by
- 6,973
- References
- 10
- Citations by year
- 2026: 367 · 2025: 539 · 2024: 532 · 2023: 534 · 2022: 464 · 2021: 498 · 2020: 563 · 2019: 412 · 2018: 395 · 2017: 383 · 2016: 290 · 2015: 270 · 2014: 221 · 2013: 228 · 2012: 165
- FWCI
- 14.72
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- Journal of Media Literacy Education (submittedVersion, cc-by)
- Funders
- National Science Foundation (7920785)
- Division of Materials Research
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Semiconductor Quantum Structures and Devices
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Surface and Thin Film Phenomena
- Keywords
- Hall conductance quantization, two-dimensional electron gas, uniform magnetic field, Kubo formula, Landau levels, quantum Hall effect
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