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Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals.
Hall Effect in Ferromagnetics
Karplus, R. & Luttinger, J · 1954
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Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
Harper, P. G · 1955
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Azbel, M. Y · 1964
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Hofstadter, D. R · 1976
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Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M · 1982
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Jaksch, D. & Zoller, P · 2003
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S. Rahav, I. Gilary, and S. Fishman, Phys. Rev. A 68
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Mueller, E. J · 2004
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Sørensen, A. S., Demler, E. & Lukin, M. D · 2005
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Lignier, H. et al · 2007
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Gauge fields for ultracold atoms in optical superlattices
Gerbier, F. & Dalibard, J · 2010
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Berry phase effects on electronic properties
Xiao, D., Chang, M.-C. & Niu, Q · 2010
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D. Xiao, M. C. Chang and Q. Niu, Rev. Mod. Phys. 82
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Synthetic Gauge Fields for Vibrational Excitations of Trapped Ions
Bermudez, A., Schaetz, T. & Porras, D · 2011
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Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice
Aidelsburger, M. et al · 2011
Cited alongside, same era.
Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
Kolovsky, A. R · 2011
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Light-induced gauge fields for ultracold atoms
Goldman, N., Juzeliunas, G., Ohberg, P. & Spielman, I. B · 2013
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Photonic Floquet topological insulators
Rechtsman, M. C. et al · 2013
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Quantum fluids of light
Carusotto, I. & Ciuti, C · 2013
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Extracting the Chern Number from the Dynamics of a Fermi Gas: Implementing a Quantum Hall Bar for Cold Atoms
Dauphin, A. & Goldman, N · 2013
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Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices
Aidelsburger, M. et al · 2013
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Direct measurement of the Zak phase in topological Bloch bands
Atala, M. et al · 2013
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Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices
Struck, J. et al · 2011
Cited alongside, same era.
Mapping the Berry curvature from semiclassical dynamics in optical lattices
Price, H. & Cooper, N · 2012
Cited alongside, same era.
Observation of a superfluid Hall effect
LeBlanc, L. J. et al · 2012
Cited alongside, same era.
Experimental Realization of Plaquette Resonating Valence-Bond States with Ultracold Atoms in Optical Superlattices
Nascimbène, S. et al · 2012
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H. M. Price and N. R. Cooper, Phys. Rev. A 85
2012
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S. Nascimbène et al
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Interferometric Approach to Measuring Band Topology in 2D Optical Lattices
Abanin, D. A., Kitagawa, T., Bloch, I. & Demler, E · 2013
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Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W · 2013
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M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y.-A. Chen, and I. Bloch, Phys. Rev. Lett. 107
2013
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A. Dauphin and N. Goldman, Phys. Rev. Lett. 111
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Dynamic Optical Superlattices with Topological Bands
Baur, S. K., Schleier-Smith, M. H. & Cooper, N. R · 2014
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Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
Goldman, N. & Dalibard, J · 2014
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Bukov, M., D’Alessio, L. & Polkovnikov, A · 2014
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Experimental realisation of the topological Haldane model
Jotzu, G. et al · 2014
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N. Goldman and J. Dalibard, Phys. Rev. X 4
2014
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