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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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“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
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“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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“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
“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]
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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
Flagged first, then by citations
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Items 501–600 of 1,008
Hasan, M. Z., Xu, S., & Bian, G. (2015) · Physica Scripta · doi:10.1088/0031-8949/2015/t164/014001 · Cited by 165
Statistical moments of quantum-walk dynamics reveal topological quantum transitions
Cardano, F., Maffei, M., Massa, F., Piccirillo, B., de Lisio, C., De Filippis, G., Cataudella, V., Santamato, E., & Marrucci, L. (2016) · Nature Communications · doi:10.1038/ncomms11439 · Cited by 152
Localization and adiabatic pumping in a generalized Aubry-André-Harper model
Liu, F., Ghosh, S., & Chong, Y. D. (2015) · Physical Review B · doi:10.1103/physrevb.91.014108 · Cited by 162
Roadmap on topological photonics
Price, H. M., Chong, Y. D., Khanikaev, A. B., Schomerus, H., Maczewsky, L. J., Kremer, M., Heinrich, M., Szameit, A., Zilberberg, O., Yang, Y., et al. (2022) · Journal of Physics Photonics · doi:10.1088/2515-7647/ac4ee4 · Cited by 166
“The origins of the field reach back to the discovery of the quantum Hall effect (QHE) in 1980 [1], and the consequent realization that electronic energy bands can be characterized by integer topological invariants [2, 3].”
BackgroundRecent progress in the theory of bulk photovoltaic effect
Dai, Z., & Rappe, A. M. (2023) · Chemical Physics Reviews · doi:10.1063/5.0101513 · Cited by 162
Measuring quantized circular dichroism in ultracold topological matter
Asteria, L., Tran, D. T., Ozawa, T., Tarnowski, M., Rem, B. S., Fläschner, N., Sengstock, K., Goldman, N., & Weitenberg, C. (2019) · Nature Physics · doi:10.1038/s41567-019-0417-8 · Cited by 184
Two-dimensional Stiefel-Whitney insulators in liganded Xenes
Pan, M., Li, D., Fan, J., & Huang, H. (2022) · npj Computational Materials · doi:10.1038/s41524-021-00695-2 · Cited by 162
Lattice generalization of the Dirac equation to general spin and the role of the flat band
Dóra, B., Kailasvuori, J., & Moessner, R. (2011) · Physical Review B · doi:10.1103/physrevb.84.195422 · Cited by 159
Homotopy characterization of non-Hermitian Hamiltonians
Wojcik, C. C., Sun, X.-Q., Bzdušek, T., & Fan, S. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.205417 · Cited by 160
Quantum Quenches in Chern Insulators
Caio, M. D., Cooper, N. R., & Bhaseen, M. J. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.236403 · Cited by 159
Jünemann, J., Piga, A., Ran, S.-J., Lewenstein, M., Rizzi, M., & Bermúdez, A. (2017) · Physical Review X · doi:10.1103/physrevx.7.031057 · Cited by 157
Exceptional links and twisted Fermi ribbons in non-Hermitian systems
Carlström, J., & Bergholtz, E. J. (2018) · Physical Review A · doi:10.1103/physreva.98.042114 · Cited by 159
Measuring quantized circular dichroism in ultracold topological matter
Asteria, L., Tran, D.-T., Ozawa, T., Tarnowski, M., Rem, B. S., Fläschner, N., Sengstock, K., Goldman, N., & Weitenberg, C. (2019) · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · Cited by 159
Classifying and measuring geometry of a quantum ground state manifold
Kolodrubetz, M., Gritsev, V., & Polkovnikov, A. (2013) · Physical Review B · doi:10.1103/physrevb.88.064304 · Cited by 158
Isolated flat bands and spin-1 conical bands in two-dimensional lattices
Green, D., Santos, L. H., & Chamon, C. (2010) · Physical Review B · doi:10.1103/physrevb.82.075104 · Cited by 156
Controlling mass and energy diffusion with metamaterials
Yang, F., Zhang, Z., Xu, L., Liu, Z., Jin, P., Zhuang, P., Lei, M., Liu, J., Jiang, J., Ouyang, X., et al. (2024) · Reviews of Modern Physics · doi:10.1103/revmodphys.96.015002 · Cited by 165
Edge Solitons of Topological Insulators and Fractionalized Quasiparticles in Two Dimensions
Lee, D. H., Zhang, G.-M., & Xiang, T. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.196805 · Cited by 153
Emergent electromagnetism in solids
Nagaosa, N., & Tokura, Y. (2012) · Physica Scripta · doi:10.1088/0031-8949/2012/t146/014020 · Cited by 158
In-Plane Magnetization-Induced Quantum Anomalous Hall Effect
Liu, X., Hsu, H.-C., & Liu, C. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.086802 · Cited by 157
Axion physics in condensed-matter systems
Nenno, D. M., Garcia, C. A. C., Gooth, J., Felser, C., & Narang, P. (2020) · Nature Reviews Physics · doi:10.1038/s42254-020-0240-2 · Cited by 162
Fractional quantum anomalous Hall states in twisted bilayer MoTe2 and WSe2
Reddy, A. P., Alsallom, F., Zhang, Y., Devakul, T., & Fu, L. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.085117 · Cited by 157
Anomalous Hall Effect –A New Perspective–
Nagaosa, N. (2006) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.75.042001 · Cited by 156
Manipulation of Dirac Cones in Mechanical Graphene
Kariyado, T., & Hatsugai, Y. (2015) · Scientific Reports · doi:10.1038/srep18107 · Cited by 157
Creation and annihilation of topological meron pairs in in-plane magnetized films
Gao, N., Je, S., Im, M., Choi, J. W., Yang, M., Li, Q., Wang, T., Lee, S., Han, H., Lee, K., et al. (2019) · Nature Communications · doi:10.1038/s41467-019-13642-z · Cited by 156
Demonstration of a quantized acoustic octupole topological insulator
Ni, X., Li, M., Weiner, M., Alù, A., & Khanikaev, A. B. (2020) · CUNY Academic Works (City University of New York) · Cited by 155
Colloquium : Atomtronic circuits: From many-body physics to quantum technologies
Luigi Amico, A., Anderson, D. Z., Boshier, M. G., Brantut, J.-P., Kwek, L. C., Minguzzi, A., & von Klitzing, W. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.041001 · Cited by 173
Topological insulators in three dimensions from spontaneous symmetry breaking
Zhang, Y., Ran, Y., & Vishwanath, A. (2009) · Physical Review B · doi:10.1103/physrevb.79.245331 · Cited by 150
Transport in two-dimensional topological materials: recent developments in experiment and theory
Culcer, D., Keser, A. C., Li, Y., & Tkachov, G. (2020) · 2D Materials · doi:10.1088/2053-1583/ab6ff7 · Cited by 164
Fractional Chern insulators and the W ∞ algebra
Parameswaran, S. A., Roy, R., & Sondhi, S. L. (2012) · Physical Review B · doi:10.1103/physrevb.85.241308 · Cited by 153
Quantum systems under frequency modulation
Silveri, M., Tuorila, J., Thuneberg, E. V., & Paraoanu, G. S. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa5170 · Cited by 157
Tan, X., Zhang, D.-W., Yang, Z., Chu, J., Zhu, Y.-Q., Li, D., Yang, X., Song, S., Han, Z., Li, Z., et al. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.210401 · Cited by 154
Periodically driven quantum matter: The case of resonant modulations
Goldman, N., Dalibard, J., Aidelsburger, M., & Cooper, N. R. (2015) · Physical Review A · doi:10.1103/physreva.91.033632 · Cited by 142
Fractional quantum Hall effect in a periodic potential
Kol, A., & Read, N. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.48.8890 · Cited by 157
Emerging magnetism and anomalous Hall effect in iridate–manganite heterostructures
Nichols, J., Gao, X., Lee, S., Meyer, T. L., Freeland, J. W., Lauter, V., Yi, D., Liu, J., Haskel, D., Petrie, J. R., et al. (2016) · Nature Communications · doi:10.1038/ncomms12721 · Cited by 152
Quantum transport in Dirac and Weyl semimetals: a review
Wang, S., Lin, B., Wang, A.-Q., Yu, D., & Liao, Z. (2017) · Advances in Physics X · doi:10.1080/23746149.2017.1327329 · Cited by 152
Observation and control of maximal Chern numbers in a chiral topological semimetal
Schröter, N. B. M., Stolz, S., Manna, K., de Juan, F., Vergniory, M. G., Krieger, J. A., Pei, D., Schmitt, T., Dudin, P., Kim, T. K., et al. (2020) · Science · doi:10.1126/science.aaz3480 · Cited by 166
Relations between topology and the quantum metric for Chern insulators
Ozawa, T., & Mera, B. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.045103 · Cited by 168
Ni, X., Yves, S., Krasnok, A., & Alù, A. (2023) · Chemical Reviews · doi:10.1021/acs.chemrev.2c00800 · Cited by 166
Real-space Berry phases: Skyrmion soccer (invited)
Everschor‐Sitte, K., & Sitte, M. (2014) · Journal of Applied Physics · doi:10.1063/1.4870695 · Cited by 153
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals
Mei, J., Chen, Z., & Wu, Y. (2016) · Scientific Reports · doi:10.1038/srep32752 · Cited by 150
Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor
Lai, S., Liu, H., Zhang, Z., Zhao, J., Feng, X., Wang, N., Tang, C., Liu, Y., Novoselov, K. S., Yang, S. A., et al. (2021) · Nature Nanotechnology · doi:10.1038/s41565-021-00917-0 · Cited by 151
Diophantine equation for the three-dimensional quantum Hall effect
Kohmoto, M., Halperin, B. I., & Wu, Y.-S. (1992) · Physical Review B · doi:10.1103/physrevb.45.13488 · Cited by 142
Self-citationAcceleration of adiabatic quantum dynamics in electromagnetic fields
Masuda, S., & Nakamura, K. (2011) · Physical Review A · doi:10.1103/physreva.84.043434 · Cited by 143
Topological Edge States in the One-Dimensional Superlattice Bose-Hubbard Model
Grusdt, F., Höning, M., & Fleischhauer, M. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.260405 · Cited by 152
Hirahara, T., Eremeev, S. V., Shirasawa, T., Okuyama, Y., Kubo, T., Nakanishi, R., Akiyama, R., Takayama, A., Hajiri, T., Ideta, S.-I., et al. (2017) · Nano Letters · doi:10.1021/acs.nanolett.7b00560 · Cited by 148
Dynamical classification of topological quantum phases
Zhang, L., Zhang, L., Niu, S., & Liu, X.-J. (2018) · 中国科学通报：英文版 · doi:10.1016/j.scib.2018.09.018 · Cited by 147
“In the last over thirty years, following the discovery of the quantum Hall effect [1,2], physicists have established a new classification of fundamental states of quantum matter, called topological quantum phases [3,4], which are beyond the scope of the celebrated Landau-Ginzburg-Wilson framework that characterizes qu…”
BackgroundInfluentialSymmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—
Mizushima, T., Tsutsumi, Y., Kawakami, T., Sato, M., Ichioka, M., & Machida, K. (2016) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.85.022001 · Cited by 148
Phase-space localization: Topological aspects of quantum chaos
Lebœuf, P., Jorge Kurchan, B., Feingold, M., & Arovas, D. P. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.3076 · Cited by 149
Topological phenomena in quantum walks: elementary introduction to the physics of topological phases
Kitagawa, T. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0425-4 · Cited by 178
Detecting Chiral Edge States in the Hofstadter Optical Lattice
Goldman, N., Beugnon, J., & Gerbier, F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.255303 · Cited by 145
Quantum Hall effect in graphene: Disorder effect and phase diagram
Sheng, D. N., Sheng, L., & Weng, Z.-Y. (2006) · Physical Review B · doi:10.1103/physrevb.73.233406 · Cited by 152
Transport in three-dimensional topological insulators: Theory and experiment
Culcer, D. (2011) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2011.11.003 · Cited by 151
Measurement of a Topological Edge Invariant in a Microwave Network
Hu, W., Pillay, J. C., Wu, K., Pasek, M., Shum, P. P., & Chong, Y. D. (2015) · Physical Review X · doi:10.1103/physrevx.5.011012 · Cited by 154
High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices
Kumar, R. K., Chen, X., Auton, G. H., Mishchenko, A., Bandurin, D. A., Morozov, S. V., Cao, Y., Khestanova, E., Shalom, M. B., Kretinin, A. V., et al. (2017) · Science · doi:10.1126/science.aal3357 · Cited by 148
Prediction of a Weyl semimetal inHg1−x−yCdxMnyTe
Bulmash, D., Liu, C.-X., & Qi, X.-L. (2014) · Physical Review B · doi:10.1103/physrevb.89.081106 · Cited by 144
Possible interaction-driven topological phases in (111) bilayers of LaNiO 3
Yang, K., Zhu, W., Xiao, D., Okamoto, S., Wang, Z., & Ran, Y. (2011) · Physical Review B · doi:10.1103/physrevb.84.201104 · Cited by 146
PT -Symmetric Real Dirac Fermions and Semimetals
Zhao, Y. X., & Lu, Y. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.056401 · Cited by 146
Lattice models with exactly solvable topological hinge and corner states
Kunst, F. K., van Miert, G. C. P., & Bergholtz, E. J. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.241405 · Cited by 147
Topological light-trapping on a dislocation
Li, F.-F., Wang, H., Xiong, Z., Lou, Q., Chen, P., Wu, R., Poo, Y., Jiang, J., & John, S. (2018) · Nature Communications · doi:10.1038/s41467-018-04861-x · Cited by 157
Circuit implementation of a four-dimensional topological insulator
Wang, Y., Price, H. M., Zhang, B., & Chong, Y. D. (2020) · RePEc: Research Papers in Economics · Cited by 147
Charge deficiency, charge transport and comparison of dimensions
Avron, J. E., Seiler, R., & Barry Simon, A. (1994) · Communications in Mathematical Physics · doi:10.1007/bf02102644 · Cited by 147
EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT
Kellendonk, J., Richter, T., & Schulz‐Baldes, H. (2002) · Reviews in Mathematical Physics · doi:10.1142/s0129055x02001107 · Cited by 146
Quantum transport in topological semimetals under magnetic fields
Lu, H., & Shen, S.-Q. (2016) · Frontiers of Physics · doi:10.1007/s11467-016-0609-y · Cited by 147
Shabbir, B., Nadeem, M., Dai, Z., Fuhrer, M. S., Xue, Q.-K., Wang, X. L., & Bao, Q. (2018) · Applied Physics Reviews · doi:10.1063/1.5040694 · Cited by 154
Topological classification of crystalline insulators with space group symmetry
Jadaun, P., Xiao, D., Niu, Q., & Banerjee, S. K. (2013) · Physical Review B · doi:10.1103/physrevb.88.085110 · Cited by 140
Anomalous Hall Effect and Skyrmion Number in Real and Momentum Spaces
Onoda, M., Tatara, G., & Nagaosa, N. (2004) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.73.2624 · Cited by 144
Quantised Hall conductance in a perfect crystal
Dana, I., Avron, J. E., & Žák, J. (1985) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/18/22/004 · Cited by 144
Localization in a Quantum Spin Hall System
Onoda, M., Avishai, Y., & Nagaosa, N. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.076802 · Cited by 145
Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
Perez-Piskunow, P. M., Torres, L. E. F. F., & Usaj, G. (2015) · Physical Review A · doi:10.1103/physreva.91.043625 · Cited by 138
Mott transition in an anyon gas
Chen, W., Fisher, M. P. A., & Wu, Y.-S. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.48.13749 · Cited by 146
Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder
Piraud, M., Heidrich‐Meisner, F., McCulloch, I. P., Greschner, S., Vekua, T., & Schollwöck, U. (2015) · Physical Review B · doi:10.1103/physrevb.91.140406 · Cited by 145
Topological phase transitions and Thouless pumping of light in photonic waveguide arrays
Ke, Y., Qin, X., Mei, F., Zhong, H., Kivshar, Y. S., & Lee, C. (2016) · Laser & Photonics Review · doi:10.1002/lpor.201600119 · Cited by 146
Shabbir, B., Nadeem, M., Dai, Z., Fuhrer, M. S., Xue, Q.-K., Wang, X. L., & Bao, Q. (2018) · Research Online (University of Wollongong) · Cited by 142
Landau level spectrum of Bloch electrons in a honeycomb lattice
Rammal, R. (1985) · Journal de physique · doi:10.1051/jphys:019850046080134500 · Cited by 142
Aoki, H. (1987) · Reports on Progress in Physics · doi:10.1088/0034-4885/50/6/002 · Cited by 142
Topological non-Hermitian origin of surface Maxwell waves
Bliokh, K. Y., Leykam, D., Lein, M., & Nori, F. (2019) · Nature Communications · doi:10.1038/s41467-019-08397-6 · Cited by 140
Probing chiral edge dynamics and bulk topology of a synthetic Hall system
Chalopin, T., Satoor, T., Evrard, A., Makhalov, V., Dalibard, J., Lopes, R., & Nascimbène, S. (2020) · Nature Physics · doi:10.1038/s41567-020-0942-5 · Cited by 147
“The relevance of the analogy is confirmed by the structure of energy bands En(p) expected for the Hamiltonian (2) describing our system, shown in Fig.”
BackgroundInfluentialQuantized nonlinear Thouless pumping
Jürgensen, M., Mukherjee, S., & Rechtsman, M. C. (2021) · RePEc: Research Papers in Economics · Cited by 141
Realizing and Detecting the Quantum Hall Effect without Landau Levels by Using Ultracold Atoms
Shao, L. B., Zhu, S.-L., Sheng, L., Xing, D. Y., & Wang, Z. D. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.246810 · Cited by 140
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Cheon, S., Kim, T.-H., Lee, S., & Yeom, H. W. (2015) · Science · doi:10.1126/science.aaa7055 · Cited by 137
Owerre, S. A. (2016) · Journal of Applied Physics · doi:10.1063/1.4959815 · Cited by 140
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Alvarez, V. M. M., & Coutinho-Filho, M. D. (2019) · Physical Review A · doi:10.1103/physreva.99.013833 · Cited by 139
Ni, X., Chen, K., Weiner, M., Apigo, D. J., Prodan, C., Alù, A., Prodan, E. V., & Khanikaev, A. B. (2019) · Communications Physics · doi:10.1038/s42005-019-0151-7 · Cited by 139
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Schröter, N., Stolz, S., Manna, K., de Juan, F., Vergniory, M. G., Krieger, J. A., Pei, D., Schmitt, T., Dudin, P., Kim, T., et al. (2020) · MPG.PuRe (Max Planck Society) · Cited by 140
Lithography with a mask of block copolymer microstructures
Harrison, C. K., Park, M. S., Chaikin, P. M., Register, R. A., & Adamson, D. H. (1998) · Journal of Vacuum Science & Technology B Microelectronics and Nanometer Structures Processing Measurement and Phenomena · doi:10.1116/1.589860 · Cited by 140
Jung, J., Zhang, F., & MacDonald, A. H. (2011) · Physical Review B · doi:10.1103/physrevb.83.115408 · Cited by 139
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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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