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 $\frac{U}{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}$.
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
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
The cited source says what the claim attributes to it.
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
The cited source says what the claim attributes to it.
In the citing paper
“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
“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]
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]
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
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
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
Flagged first, then by citations
Cited by
Sorted by citations
Items 301–400 of 1,008
Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
Bauer, B., Cincio, Ł., Keller, B. P., Dolfi, M., Vidal, G., Trebst, S., & Ludwig, A. W. W. (2014) · Nature Communications · doi:10.1038/ncomms6137 · Cited by 278
Topological Phases of Sound and Light
Peano, V., Brendel, C., Schmidt, M., & Marquardt, F. (2015) · Physical Review X · doi:10.1103/physrevx.5.031011 · Cited by 387
Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
Kawabata, K., Higashikawa, S., Gong, Z., Ashida, Y., & Ueda, M. (2019) · Nature Communications · doi:10.1038/s41467-018-08254-y · Cited by 286
Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals
Onoda, M., & Nagaosa, N. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.206601 · Cited by 268
Hall viscosity, orbital spin, and geometry: Paired superfluids and quantum Hall systems
Read, N., & Rezayi, E. H. (2011) · Physical Review B · doi:10.1103/physrevb.84.085316 · Cited by 276
Electronic properties of graphene/hexagonal-boron-nitride moiré superlattice
Moon, P., & Koshino, M. (2014) · Physical Review B · doi:10.1103/physrevb.90.155406 · Cited by 260
Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study
Feng, W., Yao, Y., Zhu, W., Zhou, J.-J., Yao, W., & Xiao, D. (2012) · Physical Review B · doi:10.1103/physrevb.86.165108 · Cited by 265
Quantization of the Hall Conductance for General, Multiparticle Schrödinger Hamiltonians
Avron, J. E., & Seiler, R. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.259 · Cited by 259
Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump
Titum, P., Berg, E., Rudner, M. S., Refael, G., & Lindner, N. H. (2016) · Physical Review X · doi:10.1103/physrevx.6.021013 · Cited by 271
Topological insulator: Spintronics and quantum computations
He, M., Sun, H., & He, Q. (2019) · Frontiers of Physics · doi:10.1007/s11467-019-0893-4 · Cited by 280
“The best known example of a topological phase is the integer quantum Hall state, whose edges can host chiral states and contribute to a quantized Hall conductivity [6, 7].”
BackgroundSimplified Topological Invariants for Interacting Insulators
Wang, Z., & Zhang, S. (2012) · Physical Review X · doi:10.1103/physrevx.2.031008 · Cited by 266
Two-Dimensional Topological Insulators: Progress and Prospects
Kou, L., Ma, Y., Sun, Z., Heine, T., & Chen, C. (2017) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.7b00222 · Cited by 266
Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
Kraus, Y. E., Ringel, Z., & Zilberberg, O. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.226401 · Cited by 262
From Luttinger liquid to non-Abelian quantum Hall states
Teo, J. C. Y., & Kane, C. L. (2014) · Physical Review B · doi:10.1103/physrevb.89.085101 · Cited by 271
General theorem relating the bulk topological number to edge states in two-dimensional insulators
Qi, X.-L., Wu, Y.-S., & Zhang, S. (2006) · Physical Review B · doi:10.1103/physrevb.74.045125 · Cited by 262
An Aharonov-Bohm interferometer for determining Bloch band topology
Duca, L., Li, T., Reitter, M., Bloch, I., Schleier-Smith, M., & Schneider, U. (2014) · Science · doi:10.1126/science.1259052 · Cited by 266
Quantum anomalous Hall effect in single-layer and bilayer graphene
Tse, W.-K., Qiao, Z., Yao, Y., MacDonald, A. H., & Niu, Q. (2011) · Physical Review B · doi:10.1103/physrevb.83.155447 · Cited by 259
Multiterminal Conductance of a Floquet Topological Insulator
Torres, L. E. F. F., Perez-Piskunow, P. M., Balseiro, C. A., & Usaj, G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.266801 · Cited by 259
Photonic topological insulator with broken time-reversal symmetry
He, C., Sun, X., Liu, X., Lu, M., Chen, Y., Feng, L., & Chen, Y. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1525502113 · Cited by 260
The Roadmap of 2D Materials and Devices Toward Chips
Liu, A., Zhang, X., Liu, Z., Li, Y., Peng, X., Li, X., Qin, Y., Chen, H., Qiu, Y., Jiang, H., et al. (2024) · Nano-Micro Letters · doi:10.1007/s40820-023-01273-5 · Cited by 274
Four-Dimensional Quantum Hall Effect with Ultracold Atoms
Price, H. M., Zilberberg, O., Ozawa, T., Carusotto, I., & Goldman, N. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.195303 · Cited by 253
Exotic electronic states in the world of flat bands: From theory to material
Liu, Z., Liu, F., & Wu, Y.-S. (2014) · Chinese Physics B · doi:10.1088/1674-1056/23/7/077308 · Cited by 254
Freed, D. S., & Moore, G. W. (2013) · Annales Henri Poincaré · doi:10.1007/s00023-013-0236-x · Cited by 248
Ding, J., Qiao, Z., Feng, W., Yao, Y., & Niu, Q. (2011) · Physical Review B · doi:10.1103/physrevb.84.195444 · Cited by 256
Zero modes of tight-binding electrons on the honeycomb lattice
Hasegawa, Y., Konno, R., Nakano, H., & Kohmoto, M. (2006) · Physical Review B · doi:10.1103/physrevb.74.033413 · Cited by 259
Self-citationSpin Hall Effects for Cold Atoms in a Light-Induced Gauge Potential
Zhu, S.-L., Fu, H., Wu, C., Zhang, S., & Duan, L.-M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.240401 · Cited by 256
Stability of the spin density wave phases in (TMTSF)2ClO4 : quantized nesting effect
Héritier, M., Montambaux, G., & Lederer, P. (1984) · Journal de Physique Lettres · doi:10.1051/jphyslet:019840045019094300 · Cited by 255
Topological pumping over a photonic Fibonacci quasicrystal
Verbin, M., Zilberberg, O., Lahini, Y., Kraus, Y. E., & Silberberg, Y. (2015) · Physical Review B · doi:10.1103/physrevb.91.064201 · Cited by 252
Universal few-body physics and cluster formation
Greene, C. H., Giannakeas, P., & Pérez‐Ríos, J. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.035006 · Cited by 250
Artificial gauge fields in materials and engineered systems
Aidelsburger, M., Nascimbène, S., & Goldman, N. (2018) · Comptes Rendus Physique · doi:10.1016/j.crhy.2018.03.002 · Cited by 260
Dielectric and ferroic properties of metal halide perovskites
Wilson, J. N., Frost, J. M., Wallace, S. K., & Walsh, A. (2019) · APL Materials · doi:10.1063/1.5079633 · Cited by 254
Riemannian geometry of resonant optical responses
Ahn, J., Guo, G.-Y., Nagaosa, N., & Vishwanath, A. (2022) · Nature Physics · doi:10.1038/s41567-021-01465-z · Cited by 252
“The real projective line RP(1) ' S(1) is the only compact and connected onedimensional manifold [1].”
BackgroundThermal Hall effect of magnons in magnets with dipolar interaction
Matsumoto, R., Shindou, R., & Murakami, S. (2014) · Physical Review B · doi:10.1103/physrevb.89.054420 · Cited by 252
Giant magnetoresistance and perfect spin filter in silicene, germanene, and stanene
Rachel, S., & Ezawa, M. (2014) · Physical Review B · doi:10.1103/physrevb.89.195303 · Cited by 249
Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects
Otrokov, M. M., Menshchikova, T. V., Vergniory, M. G., Rusinov, I. P., Vyazovskaya, A. Y., Koroteev, Y. M., Bihlmayer, G., Ernst, A., Echenique, P. M., Arnau, A., et al. (2017) · 2D Materials · doi:10.1088/2053-1583/aa6bec · Cited by 247
Weyl semimetals from noncentrosymmetric topological insulators
Liu, J., & Vanderbilt, D. (2014) · Physical Review B · doi:10.1103/physrevb.90.155316 · Cited by 244
Zero-Field Skyrmions with a High Topological Number in Itinerant Magnets
Ozawa, R., Hayami, S., & Motome, Y. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.147205 · Cited by 246
Carbon- and Nitrogen-Based Organic Frameworks
Sakaushi, K., & Antonietti, M. (2015) · Accounts of Chemical Research · doi:10.1021/acs.accounts.5b00010 · Cited by 247
Fukui, T., & Hatsugai, Y. (2007) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.76.053702 · Cited by 243
Topological Phononics: From Fundamental Models to Real Materials
Liu, Y., Chen, X., & Xu, Y. (2019) · Advanced Functional Materials · doi:10.1002/adfm.201904784 · Cited by 245
Chirality-Driven Anomalous Hall Effect in Weak Coupling Regime
Tatara, G., & Kawamura, H. (2002) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.71.2613 · Cited by 244
Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface
Zhong, S., Moore, J. E., & Souza, I. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.077201 · Cited by 253
Hermele, M., Gurarie, V., & Rey, A. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.135301 · Cited by 247
Topological phases for fermionic cold atoms on the Lieb lattice
Goldman, N., Urban, D. F., & Bercioux, D. (2011) · Physical Review A · doi:10.1103/physreva.83.063601 · Cited by 241
Progress and perspectives on phononic crystals
Vasileiadis, T., Varghese, J., Babačić, V., Gomis‐Brescó, J., Navarro‐Urrios, D., & Graczykowski, B. (2021) · Journal of Applied Physics · doi:10.1063/5.0042337 · Cited by 247
A second wave of topological phenomena in photonics and acoustics
Zhang, X., Zangeneh-Nejad, F., Chen, Z.-G., Lu, M.-H., & Christensen, J. (2023) · Nature · doi:10.1038/s41586-023-06163-9 · Cited by 240
Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response
Hosur, P. (2011) · Physical Review B · doi:10.1103/physrevb.83.035309 · Cited by 258
Evidence of Hofstadter's Fractal Energy Spectrum in the Quantized Hall Conductance
Albrecht, C., Smet, J. H., von Klitzing, K., Weiß, D., Umansky, V., & Schweizer, H. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.147 · Cited by 239
Spin-valley coupling in a two-dimensional V Si 2 N 4 monolayer
Cui, Q., Zhu, Y., Liang, J., Cui, P., & Yang, H. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.085421 · Cited by 239
Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology
Wang, H.-X., Guo, G.-Y., & Jiang, J. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab3f71 · Cited by 238
Quantum simulation with interacting photons
Hartmann, M. J. (2016) · Journal of Optics · doi:10.1088/2040-8978/18/10/104005 · Cited by 237
Qi, X.-L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.126803 · Cited by 237
A Short Introduction to Topological Quantum Computation
Lahtinen, V., & Pachos, J. K. (2017) · SciPost Physics · doi:10.21468/scipostphys.3.3.021 · Cited by 288
Aguilar, R. V., Stier, A. V., Liu, W., Bilbro, L. S., George, D., Bansal, N., Wu, L., Černe, J., Markelz, A. G., Oh, S., et al. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.087403 · Cited by 234
Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator
Dehghani, H., Oka, T., & Mitra, A. (2015) · Physical Review B · doi:10.1103/physrevb.91.155422 · Cited by 227
Topology and Broken Symmetry in Floquet Systems
Harper, F., Roy, R., Rudner, M. S., & Sondhi, S. L. (2019) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031218-013721 · Cited by 229
Intelligent infrared sensing enabled by tunable moiré quantum geometry
Ma, C., Yuan, S., Cheung, P., Watanabe, K., Taniguchi, T., Zhang, F., & Xia, F. (2022) · Nature · doi:10.1038/s41586-022-04548-w · Cited by 246
Quantum Hall physics: Hierarchies and conformal field theory techniques
Hansson, T. H., Hermanns, M., Simon, S. H., & Viefers, S. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.025005 · Cited by 240
Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
Kawabata, K., Higashikawa, S., Gong, Z., Ashida, Y., & Ueda, M. (2019) · RePEc: Research Papers in Economics · Cited by 233
Ab initio tight-binding Hamiltonian for transition metal dichalcogenides
Fang, S., Defo, R. K., Shirodkar, S. N., Lieu, S., Tritsaris, G. A., & Kaxiras, E. (2015) · Physical Review B · doi:10.1103/physrevb.92.205108 · Cited by 238
2D layered transition metal dichalcogenides (MoS2): Synthesis, applications and theoretical aspects
Singh, A. K., Kumar, P., Late, D. J., Kumar, A., Patel, S. J., & Singh, J. N. (2018) · Applied Materials Today · doi:10.1016/j.apmt.2018.09.003 · Cited by 237
Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene
Saito, Y., Ge, J., Rademaker, L., Watanabe, K., Taniguchi, T., Abanin, D. A., & Young, A. F. (2021) · Nature Physics · doi:10.1038/s41567-020-01129-4 · Cited by 231
K-theory of C*—Algebras in solid state physics
Bellissard, J. (2008) · Springer eBooks · doi:10.1007/3-540-16777-3_74 · Cited by 232
Breaking the barriers: advances in acoustic functional materials
Ge, H., Yang, M., Ma, C., Lu, M., Chen, Y., Fang, N. X., & Sheng, P. (2017) · National Science Review · doi:10.1093/nsr/nwx154 · Cited by 229
Topological origin of equatorial waves
Delplace, P., Marston, J. B., & Venaille, A. (2017) · Science · doi:10.1126/science.aan8819 · Cited by 227
Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
Wen, J., Rüegg, A., Wang, C. ‐. J., & Fiete, G. A. (2010) · Physical Review B · doi:10.1103/physrevb.82.075125 · Cited by 225
Topological Insulators in Amorphous Systems
Agarwala, A., & Shenoy, V. B. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.236402 · Cited by 236
Axion electrodynamics in topological materials
Sekine, A., & Nomura, K. (2021) · Journal of Applied Physics · doi:10.1063/5.0038804 · Cited by 240
Experimental measurement of the Berry curvature from anomalous transport
Wimmer, M., Price, H. M., Carusotto, I., & Peschel, U. (2017) · Nature Physics · doi:10.1038/nphys4050 · Cited by 225
Theory of topological spin current in noncentrosymmetric superconductors
Tanaka, Y., Yokoyama, T., Balatsky, A. V., & Nagaosa, N. (2009) · Physical Review B · doi:10.1103/physrevb.79.060505 · Cited by 222
Hamiltonian theories of the fractional quantum Hall effect
Murthy, G. N., & Shankar, R. (2003) · Reviews of Modern Physics · doi:10.1103/revmodphys.75.1101 · Cited by 237
Impurity-bound states and Green's function zeros as local signatures of topology
Slager, R.-J., Rademaker, L., Zaanen, J., & Balents, L. (2015) · Physical Review B · doi:10.1103/physrevb.92.085126 · Cited by 217
Tight-Binding Modeling and Low-Energy Behavior of the Semi-Dirac Point
Banerjee, S., Singh, R. R. P., Pardo, V., & Pickett, W. E. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.016402 · Cited by 220
Chern invariants for continuous media
Silveirinha, M. G. (2015) · Physical Review B · doi:10.1103/physrevb.92.125153 · Cited by 223
Topological Acoustic Delay Line
Zhang, Z., Tian, Y., Cheng, Y., Wei, Q., Liu, X., & Christensen, J. (2018) · Physical Review Applied · doi:10.1103/physrevapplied.9.034032 · Cited by 221
Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
Bzdušek, T., & Sigrist, M. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.155105 · Cited by 225
Moiré butterflies in twisted bilayer graphene
Bistritzer, R., & MacDonald, A. H. (2011) · Physical Review B · doi:10.1103/physrevb.84.035440 · Cited by 220
Observation of topological transitions in interacting quantum circuits
Roushan, P., Neill, C., Chen, Y., Kolodrubetz, M., Quintana, C., Leung, N., Fang, M., Barends, R., Campbell, B., Chen, Z., et al. (2014) · Nature · doi:10.1038/nature13891 · Cited by 219
Gradhand, M., Fedorov, D. V., Pientka, F., Zahn, P. K., Mertig, I., & Gyorffy, B. L. (2012) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/24/21/213202 · Cited by 213
Correlation effects in two-dimensional topological insulators
Hohenadler, M., & Assaad, F. F. (2013) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/25/14/143201 · Cited by 230
Topological triple phase transition in non-Hermitian Floquet quasicrystals
Weidemann, S., Kremer, M., Longhi, S., & Szameit, A. (2022) · Nature · doi:10.1038/s41586-021-04253-0 · Cited by 217
“One can further conclude from equation (3) that the triple phase transition shows a fundamental duality between Hermitian and non-Hermitian parameters, as it can be induced by changing either the site coupling β or the non-Hermitian gauge field h.”
BackgroundTopological states of condensed matter
Wang, J., & Zhang, S. (2017) · Nature Materials · doi:10.1038/nmat5012 · Cited by 217
Topological Materials: Quantum Anomalous Hall System
He, K., Wang, Y., & Xue, Q. (2018) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-033117-054144 · Cited by 213
Roadmap on Atomtronics: State of the art and perspective
Luigi Amico, A., Boshier, M. G., Birkl, G., Minguzzi, A., Miniatura, C., Kwek, L. C., Aghamalyan, D., Ahufinger, V., Anderson, D. Z., Andrei, N., et al. (2021) · AVS Quantum Science · doi:10.1116/5.0026178 · Cited by 241
Intrinsic anomalous valley Hall effect in single-layer N b 3 I 8
Peng, R., Ma, Y., Xu, X., He, Z., Huang, B., & Dai, Y. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.035412 · Cited by 214
Monolayer films of diblock copolymer microdomains for nanolithographic applications
Mansky, P. A., haikin, P., & Thomas, E. L. (1995) · Journal of Materials Science · doi:10.1007/bf00353023 · Cited by 214
Maciejko, J., Hughes, T. L., & Zhang, S. (2011) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-062910-140538 · Cited by 220
A Topological Look at the Quantum Hall Effect
Avron, J. E., Osadchy, D., & Seiler, R. (2003) · Physics Today · doi:10.1063/1.1611351 · Cited by 211
Topological Waves in Fluids with Odd Viscosity
Souslov, A., Dasbiswas, K., Fruchart, M., Vaikuntanathan, S., & Vitelli, V. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.128001 · Cited by 205
Observation of a Higher-Order Topological Bound State in the Continuum
Cerjan, A., Jürgensen, M., Benalcazar, W. A., Mukherjee, S., & Rechtsman, M. C. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.213901 · Cited by 214
Evidence for a fractional fractal quantum Hall effect in graphene superlattices
Wang, L., Gao, Y., Wen, B., Han, Z., Taniguchi, T., Watanabe, K., Koshino, M., Hone, J., & Dean, C. R. (2015) · Science · doi:10.1126/science.aad2102 · Cited by 206
Numerical study of symmetry effects on localization in two dimensions
Ando, T. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.40.5325 · Cited by 210
Observation of quadrupole transitions and edge mode topology in an LC circuit network
Serra‐Garcia, M., Süsstrunk, R., & Huber, S. D. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.020304 · Cited by 204
DeGottardi, W., Thakurathi, M., Vishveshwara, S., & Sen, D. (2013) · Physical Review B · doi:10.1103/physrevb.88.165111 · Cited by 204
Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state
Wang, J., Lian, B., Qi, X.-L., & Zhang, S. (2015) · Physical Review B · doi:10.1103/physrevb.92.081107 · Cited by 206
Recent Advances in Graphene-like 2D Materials for Spintronics Applications
Choudhuri, I., Bhauriyal, P., & Pathak, B. (2019) · Chemistry of Materials · doi:10.1021/acs.chemmater.9b02243 · Cited by 205
Floquet topological insulators
Cayssol, J., Dóra, B., Simon, F., & Moessner, R. (2013) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 208
Fuchs, J.-N., Piéchon, F., Goerbig, M. O., & Montambaux, G. (2010) · The European Physical Journal B · doi:10.1140/epjb/e2010-00259-2 · Cited by 207
Topological Charge Pumping in a One-Dimensional Optical Lattice
Wang, L., Troyer, M., & Dai, X. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.026802 · Cited by 206
Topological strong-field physics on sub-laser-cycle timescale
Silva, R. E. F., Jiménez-Galán, Á., Amorim, B., Smirnova, O. V., & Ivanov, M. (2019) · Nature Photonics · doi:10.1038/s41566-019-0516-1 · Cited by 207
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
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
