Artificial gauge fields are currently realized in a wide range of physical settings. This includes solid-state devices but also engineered systems, such as photonic crystals, ultracold gases and mechanical setups. It is the aim of this review to offer, for the first time, a unified view on these various forms of artificial electromagnetic fields and spin–orbit couplings for matter and light. This topical review provides a general introduction to the universal concept of engineered gauge fields, in a form that is accessible to young researchers entering the field. Moreover, this work aims to connect different communities, by revealing explicit links between the diverse forms and realizations of artificial gauge fields.
Les champs de jauge artificiels sont aujourd'hui réalisés dans une large gamme d'environnements physiques. Ceci inclut les dispositifs relatifs à la physique de l'état solide, mais aussi les systèmes « synthétiques » tels que les cristaux photoniques, les gaz ultrafroids et les systèmes mécaniques. C'est l'objet de cette revue d'offrir, pour la première fois, une vision unifiée de ces diverses formes de champs électromagnétiques artificiels et de couplages spin-orbite pour la matière et la lumière. Cette revue d'actualité fournit une introduction générale au concept universel de champ de jauge artificiel, dans une forme qui soit accessible aux jeunes chercheurs abordant le domaine. De plus, ce travail ambitionne de connecter différentes communautés, en révélant les liens explicites entre les différentes formes et réalisations de champs de jauge artificiels.
Mot clés : Champs de jauge, Simulation quantique, Matière condensée
Monika Aidelsburger 1, 2, 3; Sylvain Nascimbene 1; Nathan Goldman 4
@article{CRPHYS_2018__19_6_394_0, author = {Monika Aidelsburger and Sylvain Nascimbene and Nathan Goldman}, title = {Artificial gauge fields in materials and engineered systems}, journal = {Comptes Rendus. Physique}, pages = {394--432}, publisher = {Elsevier}, volume = {19}, number = {6}, year = {2018}, doi = {10.1016/j.crhy.2018.03.002}, language = {en}, }
TY - JOUR AU - Monika Aidelsburger AU - Sylvain Nascimbene AU - Nathan Goldman TI - Artificial gauge fields in materials and engineered systems JO - Comptes Rendus. Physique PY - 2018 SP - 394 EP - 432 VL - 19 IS - 6 PB - Elsevier DO - 10.1016/j.crhy.2018.03.002 LA - en ID - CRPHYS_2018__19_6_394_0 ER -
Monika Aidelsburger; Sylvain Nascimbene; Nathan Goldman. Artificial gauge fields in materials and engineered systems. Comptes Rendus. Physique, Volume 19 (2018) no. 6, pp. 394-432. doi : 10.1016/j.crhy.2018.03.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.03.002/
[1] Significance of electromagnetic potentials in the quantum theory, Phys. Rev., Volume 115 (1959) no. 3, p. 485
[2] Concept of nonintegrable phase factors and global formulation of gauge fields, Phys. Rev. D, Volume 12 (1975) no. 12, p. 3845
[3] Holonomy, the quantum adiabatic theorem, and Berry's phase, Phys. Rev. Lett., Volume 51 (1983) no. 24, p. 2167
[4] Geometry, Topology and Physics, CRC Press, 2003
[5] Generalized theory of interference and its applications, Proceedings of the Indian Academy of Sciences-Section A, vol. 44, Springer, 1956, pp. 398-417
[6] On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei, J. Chem. Phys., Volume 70 (1979) no. 5, pp. 2284-2296
[7] Quantal phase factors accompanying adiabatic changes, Proc. R. Soc., Math. Phys. Eng. Sci., vol. 392, The Royal Society, 1984, pp. 45-57
[8] Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett., Volume 49 (1982), pp. 405-408
[9] Zero modes and the quantized Hall conductance of the two-dimensional lattice in a magnetic field, Phys. Rev. B, Volume 39 (1989) no. 16
[10] Topological Insulators and Topological Superconductors, Princeton University Press, 2013
[11] Colloquium, Rev. Mod. Phys., Volume 83 (2011), pp. 1523-1543
[12] Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys., Volume 77 (2014) no. 12
[13] Introduction to the physics of artificial gauge fields | arXiv
[14] Degenerate quantum gases with spin–orbit coupling: a review, Rep. Prog. Phys., Volume 78 (2015) no. 2
[15] Topological quantum matter with ultracold gases in optical lattices, Nat. Phys., Volume 12 (2016) no. 7, pp. 639-645
[16] Topological bands for ultracold atoms, 2018 | arXiv
[17] Topological photonics, Nat. Photonics, Volume 8 (2014) no. 11, pp. 821-829
[18] Synthetic gauge fields with photons, Int. J. Mod. Phys. B, Volume 28 (2014) no. 02
[19] Topological photonics, 2018 | arXiv
[20] Topological mechanics, Nat. Phys., Volume 12 (2016) no. 7, pp. 621-623
[21] The electronic properties of graphene, Rev. Mod. Phys., Volume 81 (2009) no. 1, pp. 109-162
[22] Gauge fields in graphene, Phys. Rep., Volume 496 (2010) no. 4–5, pp. 109-148
[23] Strain engineering of graphene: a review, Nanoscale, Volume 8 (2016), p. 3207
[24] Novel effects of strains in graphene and other two dimensional materials, Phys. Rep., Volume 617 (2016), pp. 1-54
[25] Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories, Ann. Phys., Volume 525 (2013) no. 10–11, pp. 777-796
[26] Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices, Rep. Prog. Phys., Volume 79 (2015) no. 1
[27] Lattice gauge theory simulations in the quantum information era, Contemp. Phys., Volume 57 (2016) no. 3, pp. 388-412
[28] Spintronics: fundamentals and applications, Rev. Mod. Phys., Volume 76 (2004), pp. 323-410
[29] Anomalous Hall effect, Rev. Mod. Phys., Volume 82 (2010), pp. 1539-1592
[30] Topological insulators and superconductors, Rev. Mod. Phys., Volume 83 (2011), p. 1057
[31] The quantized Hall effect, Rev. Mod. Phys., Volume 58 (1986), pp. 519-531
[32] Colloquium: topological insulators, Rev. Mod. Phys., Volume 82 (2010), p. 3045
[33] Faraday effect in solids, Phys. Rev. A, Volume 137 (1965) no. 2, p. A448
[34] Photovoltaic Hall effect in graphene, Phys. Rev. B, Volume 79 (2009)
[35] Phys. Rev. B, 84 (2011)
[36] Floquet topological insulator in semiconductor quantum wells, Nat. Phys., Volume 7 (2011), pp. 490-495
[37] Floquet topological insulators, Phys. Status Solidi RRL, Volume 7 (2013), pp. 101-108
[38] Photonic Floquet topological insulators, Nature, Volume 496 (2013) no. 7444, pp. 196-200
[39] Experimental realization of the topological haldane model with ultracold fermions, Nature, Volume 515 (2014), p. 237
[40] Quantized circular photogalvanic effect in Weyl semimetals, Nat. Commun., Volume 8 (2017)
[41] Probing topology by ‘heating’: quantized circular dichroism in ultracold atoms, Sci. Adv., Volume 3 (2017) no. 8
[42] The geometric phase in molecular systems, Rev. Mod. Phys., Volume 64 (1992), pp. 51-85
[43] Berry phase effects on electronic properties, Rev. Mod. Phys., Volume 82 (2010) no. 3, p. 1959
[44] Appearance of gauge structure in simple dynamical systems, Phys. Rev. Lett., Volume 52 (1984) no. 24, p. 2111
[45] The effect of a magnetic field on electrons in a periodic potential, Phys. Rev., Volume 84 (1951), pp. 814-817
[46] Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B, Volume 14 (1976), pp. 2239-2249
[47] Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008) no. 3, p. 885
[48] Topological states in photonic systems, Nat. Phys., Volume 12 (2016) no. 7, pp. 626-629
[49] An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys., Volume 51 (1979) no. 4, p. 659
[50] The lattice gauge theory approach to quantum chromodynamics, Rev. Mod. Phys., Volume 55 (1983) no. 3, p. 775
[51] Cold bosonic atoms in optical lattices, Phys. Rev. Lett., Volume 81 (1998) no. 15, p. 3108
[52] The Oxford Solid State Basics, OUP Oxford, 2013
[53] Fractional quantum Hall physics in topological flat bands, C. R. Physique, Volume 14 (2013) no. 9–10, pp. 816-839
[54] Topological characterization of periodically-driven quantum systems, Phys. Rev. B, Volume 82 (2010)
[55] Periodically driven quantum systems: effective Hamiltonians and engineered gauge fields, Phys. Rev. X, Volume 4 (2014)
[56] Adv. Phys., 64 (2015), pp. 139-226
[57] Colloquium: atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys., Volume 89 (2017) no. 1
[58] Phys. Rev. A, 68 (2003)
[59] Periodically driven quantum matter: the case of resonant modulations, Phys. Rev. A, Volume 91 (2015) no. 3
[60] New J. Phys., 17 (2015)
[61] Brillouin–Wigner theory for high-frequency expansion in periodically driven systems: application to Floquet topological insulators, Phys. Rev. B, Volume 93 (2016)
[62] Fractional quantum Hall states of atoms in optical lattices, Phys. Rev. Lett., Volume 94 (2005) no. 8
[63] Creating artificial magnetic fields for cold atoms by photon-assisted tunneling, Europhys. Lett., Volume 93 (2011)
[64] Synthetic Gauge fields for vibrational excitations of trapped ions, Phys. Rev. Lett., Volume 107 (2011) no. 15
[65] Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices, Phys. Rev. Lett., Volume 111 (2013)
[66] Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett., Volume 111 (2013)
[67] Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms, Nat. Phys., Volume 11 (2014), p. 3171
[68] Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice, New J. Phys., Volume 18 (2016) no. 9
[69] Microscopy of the interacting Harper–Hofstadter model in the few-body limit, Nature, Volume 546 (2017), pp. 519-523
[70] Non-Abelian gauge fields and topological insulators in shaken optical lattices, Phys. Rev. Lett., Volume 109 (2012)
[71] Atomic spin–orbit coupling synthesized with magnetic-field-gradient pulses, Phys. Rev. A, Volume 87 (2013) no. 6
[72] Magnetically generated spin–orbit coupling for ultracold atoms, Phys. Rev. Lett., Volume 111 (2013) no. 12
[73] Vortices in a trapped dilute Bose–Einstein condensate, J. Phys. Condens. Matter, Volume 13 (2001) no. 12, p. R135
[74] Rotating trapped Bose–Einstein condensates, Rev. Mod. Phys., Volume 81 (2009) no. 2, pp. 647-691
[75] Quantized Vortices in Helium II, vol. 2, Cambridge University Press, 1991
[76] Superfluidity and Superconductivity, CRC Press, 1990
[77] Vortex formation in a stirred Bose–Einstein condensate, Phys. Rev. Lett., Volume 84 (2000) no. 5, pp. 806-809
[78] Observation of vortex lattices in Bose–Einstein condensates, Science, Volume 292 (2001) no. 5516, pp. 476-479
[79] Vortices and superfluidity in a strongly interacting Fermi gas, Nature, Volume 435 (2005) no. 7045, pp. 1047-1051
[80] Theoretical progress in many-body physics with ultracold dipolar gases, Phys. Rep., Volume 464 (2008) no. 3, pp. 71-111
[81] The physics of dipolar bosonic quantum gases, Rep. Prog. Phys., Volume 72 (2009) no. 12
[82] Spinor Bose–Einstein condensates, Phys. Rep., Volume 520 (2012) no. 5, pp. 253-381
[83] Spinor Bose gases: symmetries, magnetism, and quantum dynamics, Rev. Mod. Phys., Volume 85 (2013) no. 3, pp. 1191-1244
[84] Vortex-lattice dynamics in rotating spinor Bose–Einstein condensates, Phys. Rev. Lett., Volume 93 (2004) no. 21
[85] Vortices in a stirred Bose–Einstein condensate, J. Mod. Opt., Volume 47 (2000) no. 14–15, pp. 2715-2723
[86] Synthetic magnetic fields for ultracold neutral atoms, Nature, Volume 462 (2009) no. 7273, pp. 628-632
[87] Rapidly rotating Bose–Einstein condensates in and near the lowest Landau level, Phys. Rev. Lett., Volume 92 (2004) no. 4
[88] Fast rotation of a Bose–Einstein condensate, Phys. Rev. Lett., Volume 92 (2004) no. 5
[89] Vortex states of rapidly rotating dilute Bose–Einstein condensates, Phys. Rev. Lett., Volume 90 (2003) no. 14
[90] Rapidly rotating atomic gases, Adv. Phys., Volume 57 (2008) no. 6, pp. 539-616
[91] Quantum phases of vortices in rotating Bose–Einstein condensates, Phys. Rev. Lett., Volume 87 (2001) no. 12
[92] The Quantum Hall Effect (R.E. Prange; S.M. Girvin; J.L. Birman; H. Faissner; J.W. Lynn, eds.), Grad. Texts Contemp. Phys., Springer New York, New York, NY, 1990
[93] Slow light in degenerate Fermi gases, Phys. Rev. Lett., Volume 93 (2004) no. 3
[94] Raman processes and effective gauge potentials, Phys. Rev. A, Volume 79 (2009) no. 6
[95] Optical flux lattices for ultracold atomic gases, Phys. Rev. Lett., Volume 106 (2011) no. 17
[96] Quantum fluids of light, Rev. Mod. Phys., Volume 85 (2013), pp. 299-366
[97] Bose–Einstein condensation of photons in an optical microcavity, Nature, Volume 468 (2010) no. 7323, pp. 545-548
[98] Engineering photonic Floquet Hamiltonians through Fabry–Pérot resonators, New J. Phys., Volume 18 (2016) no. 3
[99] Synthetic Landau levels for photons, Nature, Volume 534 (2016), pp. 671-675
[100] Synthetic gauge fields for light beams in optical resonators, Opt. Lett., Volume 40 (2015) no. 13, pp. 2941-2944
[101] Synthetic magnetism for photon fluids, Phys. Rev. A, Volume 94 (2016)
[102] Cooperative atom–light interaction in a blockaded Rydberg ensemble, Phys. Rev. Lett., Volume 105 (2010) no. 19
[103] Photon–photon interactions via Rydberg blockade, Phys. Rev. Lett., Volume 107 (2011) no. 13
[104] Quantum nonlinear optics with single photons enabled by strongly interacting atoms, Nature, Volume 488 (2012) no. 7409, pp. 57-60
[105] Attractive photons in a quantum nonlinear medium, Nature, Volume 502 (2013) no. 7469, pp. 71-75
[106] Electrically tunable artificial gauge potential for polaritons, Nat. Commun., Volume 8 (2017)
[107] et al. Bose–Einstein condensation of exciton polaritons, Nature, Volume 443 (2006) no. 7110, pp. 409-414
[108] Bose–Einstein condensation of microcavity polaritons in a trap, Science, Volume 316 (2007) no. 5827, pp. 1007-1010
[109] Condensation of semiconductor microcavity exciton-polaritons, Science, Volume 298 (2002) no. 5591, pp. 199-202
[110] Exciton-polariton Bose–Einstein condensation, Rev. Mod. Phys., Volume 82 (2010) no. 2, p. 1489
[111] Exciton-polariton condensates, Nat. Phys., Volume 10 (2014) no. 11, pp. 803-813
[112] Superfluidity of polaritons in semiconductor microcavities, Nat. Phys., Volume 5 (2009) no. 11, pp. 805-810
[113] et al. Collective fluid dynamics of a polariton condensate in a semiconductor microcavity, Nature, Volume 457 (2009) no. 7227, pp. 291-295
[114] Quantized vortices in an exciton-polariton condensate, Nat. Phys., Volume 4 (2008) no. 9, pp. 706-710
[115] Observation of half-quantum vortices in an exciton-polariton condensate, Science, Volume 326 (2009) no. 5955, pp. 974-976
[116] et al. Persistent currents and quantized vortices in a polariton superfluid, Nat. Phys., Volume 6 (2010) no. 7, pp. 527-533
[117] Single vortex–antivortex pair in an exciton-polariton condensate, Nat. Phys., Volume 7 (2011) no. 2, pp. 129-133
[118] et al. Polariton superfluids reveal quantum hydrodynamic solitons, Science, Volume 332 (2011) no. 6034, pp. 1167-1170
[119] Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid, Nat. Phys., Volume 7 (2011) no. 8, pp. 635-641
[120] Dark-state polaritons for multicomponent and stationary light fields, Phys. Rev. A, Volume 77 (2008) no. 6
[121] Stationary pulses of light in an atomic medium, Nature, Volume 426 (2003) no. 6967, pp. 638-641
[122] Effective magnetic fields for stationary light, Phys. Rev. Lett., Volume 104 (2010) no. 3
[123] Tunable atomic spin–orbit coupling synthesized with a modulating gradient magnetic field, Sci. Rep., Volume 6 (2016)
[124] Single band motion of conduction electrons in a uniform magnetic field, Proc. Phys. Soc. A, Volume 68 (1955) no. 10, pp. 874-878
[125] Energy spectrum of a conduction electron in a magnetic field, Sov. Phys. JETP, Volume 19 (1964), p. 634
[126] Magnetoresistance oscillations in a grid potential: indication of a Hofstadter-type energy spectrum, Phys. Rev. B, Volume 43 (1991) no. 6, pp. 5192-5195
[127] Novel magneto-resistance oscillations in laterally modulated two-dimensional electrons with 20 nm periodicity formed on vicinal GaAs (111) B substrates, Physica E, Low-Dimens. Syst. Nanostruct., Volume 2 (1998) no. 1–4, pp. 944-948
[128] Fermiology of two-dimensional lateral superlattices, Phys. Rev. Lett., Volume 83 (1999) no. 11, pp. 2234-2237
[129] Landau subbands generated by a lateral electrostatic superlattice – chasing the Hofstadter butterfly, Semicond. Sci. Technol., Volume 11 (1996) no. 11S, pp. 1582-1585
[130] Evidence of Hofstadter's fractal energy spectrum in the quantized Hall conductance, Phys. Rev. Lett., Volume 86 (2001) no. 1, pp. 147-150
[131] Detection of a Landau band-coupling-induced rearrangement of the Hofstadter butterfly, Phys. Rev. Lett., Volume 92 (2004) no. 25
[132] Laterally modulated 2D electron system in the extreme quantum limit, Phys. Rev. Lett., Volume 92 (2004) no. 3
[133] Hofstadter's butterfly and the fractal quantum Hall effect in moiré superlattices, Nature, Volume 497 (2013) no. 7451, pp. 598-602
[134] Cloning of Dirac fermions in graphene superlattices, Nature, Volume 497 (2013) no. 7451, pp. 594-597
[135] Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure, Science, Volume 340 (2013) no. 6139, pp. 1427-1430
[136] Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands, Phys. Rev. B, Volume 53 (1996) no. 11, pp. 7010-7023
[137] New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett., Volume 45 (1980) no. 6, pp. 494-497
[138] Chern number and edge states in the integer quantum Hall effect, Phys. Rev. Lett., Volume 71 (1993) no. 22, pp. 3697-3700
[139] Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function, Phys. Rev. B, Volume 48 (1993) no. 16, pp. 11851-11862
[140] General theorem relating the bulk topological number to edge states in two-dimensional insulators, Phys. Rev. B, Volume 74 (2006) no. 4
[141] Quantum spin Hall effect, Phys. Rev. Lett., Volume 96 (2006) no. 10
[142] Realistic time-reversal invariant topological insulators with neutral atoms, Phys. Rev. Lett., Volume 105 (2010) no. 25
[143] Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett., Volume 100 (2008) no. 1
[144] Analogs of quantum-Hall-effect edge states in photonic crystals, Phys. Rev. A, Volume 78 (2008) no. 3
[145] Reflection-free one-way edge modes in a gyromagnetic photonic crystal, Phys. Rev. Lett., Volume 100 (2008) no. 1
[146] Observation of unidirectional backscattering-immune topological electromagnetic states, Nature, Volume 461 (2009) no. 7265, pp. 772-775
[147] Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces, Appl. Phys. Lett., Volume 97 (2010) no. 4
[148] Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides, Appl. Phys. Lett., Volume 98 (2011) no. 21
[149] Multimode one-way waveguides of large Chern numbers, Phys. Rev. Lett., Volume 113 (2014) no. 11
[150] Experimental observation of large Chern numbers in photonic crystals, Phys. Rev. Lett., Volume 115 (2015) no. 25
[151] Microwave realization of the Hofstadter butterfly, Phys. Rev. Lett., Volume 80 (1998) no. 15, pp. 3232-3235
[152] Time-and site-resolved dynamics in a topological circuit, Phys. Rev. X, Volume 5 (2015) no. 2
[153] Realizing effective magnetic field for photons by controlling the phase of dynamic modulation, Nat. Photonics, Volume 6 (2012) no. 11, pp. 782-787
[154] Chiral ground-state currents of interacting photons in a synthetic magnetic field, Nat. Phys., Volume 13 (2017) no. 2, pp. 146-151
[155] Experimental demonstration of a photonic Aharonov–Bohm effect at radio frequencies, Phys. Rev. B, Volume 87 (2013) no. 6
[156] Quarter-flux Hofstadter lattice in qubit-compatible microwave cavity array, Phys. Rev. A, Volume 97 (2018)
[157] Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature, Volume 431 (2004) no. 7005, pp. 162-167
[158] Engineering topological many-body materials in microwave cavity arrays, Phys. Rev. X, Volume 6 (2016) no. 4
[159] Observation of vortex pinning in Bose–Einstein condensates, Phys. Rev. Lett., Volume 97 (2006) no. 24
[160] Excitation of a d-density wave in an optical lattice with driven tunneling, Phys. Rev. Lett., Volume 99 (2007) no. 11
[161] Observation of vortex nucleation in a rotating two-dimensional lattice of Bose–Einstein condensates, Phys. Rev. Lett., Volume 104 (2010) no. 5
[162] Cold atoms in a rotating optical lattice with nearest-neighbor interactions, Phys. Rev. A, Volume 82 (2010) no. 6
[163] Rotating few-body atomic systems in the fractional quantum Hall regime | arXiv
[164] Phonon-induced artificial magnetic fields in optical lattices, Europhys. Lett., Volume 85 (2009) no. 1
[165] Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms, New J. Phys., Volume 5 (2003) no. 1, p. 56
[166] Particle number fractionalization of an atomic Fermi–Dirac gas in an optical lattice, Phys. Rev. Lett., Volume 88 (2002) no. 18
[167] Artificial electromagnetism for neutral atoms: Escher staircase and laughlin liquids, Phys. Rev. A, Volume 70 (2004) no. 4
[168] Gauge fields for ultracold atoms in optical superlattices, New J. Phys., Volume 12 (2010) no. 3
[169] Comment on “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling” by Kolovsky A. R., Europhys. Lett., Volume 101 (2013) no. 4
[170] Experimental realization of strong effective magnetic fields in an optical lattice, Phys. Rev. Lett., Volume 107 (2011) no. 25
[171] Observation of chiral currents with ultracold atoms in bosonic ladders, Nat. Phys., Volume 10 (2014), p. 588
[172] Observation of Bose–Einstein condensation in a strong synthetic magnetic field, Nat. Phys., Volume 11 (2015) no. 10, pp. 859-864
[173] Extracting the Chern number from the dynamics of a Fermi gas: implementing a quantum Hall bar for cold atoms, Phys. Rev. Lett., Volume 111 (2013) no. 13
[174] Measurement of Chern numbers through center-of-mass responses, Phys. Rev. B, Volume 93 (2016) no. 24
[175] Loading ultracold gases in topological Floquet bands: the fate of current and center-of-mass responses, 2D Mater., Volume 4 (2017)
[176] Photon-assisted-tunneling toolbox for quantum simulations in ion traps, New J. Phys., Volume 14 (2012) no. 5
[177] Quantization of particle transport, Phys. Rev. B, Volume 27 (1983) no. 10, p. 6083
[178] Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction, J. Phys. A, Math. Gen., Volume 17 (1984) no. 12, p. 2453
[179] Towards a quantum pump of electric charges, Phys. Rev. Lett., Volume 64 (1990) no. 15, p. 1812
[180] Topological equivalence between the Fibonacci quasicrystal and the Harper model, Phys. Rev. Lett., Volume 109 (2012) no. 11
[181] Topological pumping over a photonic Fibonacci quasicrystal, Phys. Rev. B, Volume 91 (2015) no. 6
[182] Experimental measurement of the Berry curvature from anomalous transport, Nat. Phys., Volume 13 (2017) no. 6, pp. 545-550
[183] A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice, Nat. Phys., Volume 12 (2016) no. 4, pp. 350-354
[184] Topological Thouless pumping of ultracold fermions, Nat. Phys., Volume 12 (2016) no. 4, pp. 296-300
[185] Geometrical pumping with a Bose–Einstein condensate, Phys. Rev. Lett., Volume 116 (2016) no. 20
[186] Spin pumping and measurement of spin currents in optical superlattices, Phys. Rev. Lett., Volume 117 (2016) no. 17
[187] Exploring 4D quantum Hall physics with a 2D topological charge pump, Nature, Volume 553 (2018), pp. 55-58
[188] Photonic topological boundary pumping as a probe of 4D quantum Hall physics, Nature, Volume 553 (2018), pp. 59-62
[189] Optical resonator analog of a two-dimensional topological insulator, Phys. Rev. Lett., Volume 110 (2013) no. 20
[190] Robust optical delay lines with topological protection, Nat. Phys., Volume 7 (2011) no. 11, pp. 907-912
[191] Measurement of a topological edge invariant in a microwave network, Phys. Rev. X, Volume 5 (2015) no. 1
[192] Imaging topological edge states in silicon photonics, Nat. Photonics, Volume 7 (2013) no. 12, pp. 1001-1005
[193] Measurement of topological invariants in a 2D photonic system, Nat. Photonics, Volume 10 (2016) no. 3, pp. 180-183
[194] Coriolis force induced topological order for classical mechanical vibrations, New J. Phys., Volume 17 (2015) no. 7
[195] Classification of topological phonons in linear mechanical metamaterials, Proc. Natl. Acad. Sci. USA, Volume 113 (2016) no. 33, p. E4767-E4775
[196] Observation of phononic helical edge states in a mechanical topological insulator, Science, Volume 349 (2015) no. 6243, pp. 47-50
[197] Topological mechanics of gyroscopic metamaterials, Proc. Natl. Acad. Sci. USA, Volume 112 (2015) no. 47, pp. 14495-14500
[198] Topological boundary modes in isostatic lattices, Nat. Phys., Volume 10 (2014) no. 1, pp. 39-45
[199] Phonons and elasticity in critically coordinated lattices, Rep. Prog. Phys., Volume 78 (2015) no. 7
[200] Topological boundary modes in jammed matter, Soft Matter, Volume 12 (2016) no. 28, pp. 6079-6087
[201] Topological modes bound to dislocations in mechanical metamaterials, Nat. Phys., Volume 11 (2015) no. 2, pp. 153-156
[202] Nonlinear conduction via solitons in a topological mechanical insulator, Proc. Natl. Acad. Sci. USA, Volume 111 (2014) no. 36, pp. 13004-13009
[203] Solitons in polyacetylene, Phys. Rev. Lett., Volume 42 (1979) no. 25, pp. 1698-1701
[204] Topological mechanisms as classical spinor fields | arXiv
[205] Selective buckling via states of self-stress in topological metamaterials, Proc. Natl. Acad. Sci. USA, Volume 112 (2015) no. 25, pp. 7639-7644
[206] Topological mechanics of origami and kirigami, Phys. Rev. Lett., Volume 116 (2016) no. 13
[207] Static non-reciprocity in mechanical metamaterials, Nature, Volume 542 (2017) no. 7642, pp. 461-464
[208] Transformable topological mechanical metamaterials, Nat. Commun., Volume 8 (2017)
[209] Dynamical Majorana edge modes in a broad class of topological mechanical systems, Nat. Commun., Volume 8 (2017)
[210] Geometric phase and band inversion in periodic acoustic systems, Nat. Phys., Volume 11 (2015) no. 3, pp. 240-244
[211] Acoustic topological insulator and robust one-way sound transport, Nat. Phys., Volume 12 (2016) no. 12, pp. 1124-1129
[212] Sound isolation and giant linear nonreciprocity in a compact acoustic circulator, Science, Volume 343 (2014) no. 6170, pp. 516-519
[213] Topological acoustics, Phys. Rev. Lett., Volume 114 (2015) no. 11
[214] Topological phonon modes and their role in dynamic instability of microtubules, Phys. Rev. Lett., Volume 103 (2009) no. 24
[215] Topological phononic crystals with one-way elastic edge waves, Phys. Rev. Lett., Volume 115 (2015) no. 10
[216] Universal quantum transducers based on surface acoustic waves, Phys. Rev. X, Volume 5 (2015) no. 3
[217] Detecting topological phases of microwave photons in a circuit quantum electrodynamics lattice, npj Quantum Inf., Volume 2 (2016)
[218] Observation of topological transitions in interacting quantum circuits, Nature, Volume 515 (2014) no. 7526, pp. 241-244
[219] Spectroscopic signatures of localization with interacting photons in superconducting qubits, Science, Volume 358 (2017) no. 6367, pp. 1175-1179
[220] Quantum simulation of an extra dimension, Phys. Rev. Lett., Volume 108 (2012) no. 13
[221] Synthetic gauge fields in synthetic dimensions, Phys. Rev. Lett., Volume 112 (2014) no. 4
[222] Visualizing edge states with an atomic Bose gas in the quantum Hall regime, Science, Volume 349 (2015) no. 6255, pp. 1514-1518
[223] Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science, Volume 349 (2015) no. 6255, pp. 1510-1513
[224] Adiabatic control of atomic dressed states for transport and sensing, Phys. Rev. A, Volume 92 (2015) no. 2
[225] Synthetic dimensions and spin–orbit coupling with an optical clock transition, Phys. Rev. Lett., Volume 117 (2016) no. 22
[226] Spin–orbit-coupled fermions in an optical lattice clock, Nature, Volume 542 (2017) no. 7639, pp. 66-70
[227] Atom-optics approach to studying transport phenomena, Phys. Rev. A, Volume 92 (2015) no. 4
[228] Atom-optics simulator of lattice transport phenomena, Phys. Rev. A, Volume 93 (2016) no. 5
[229] Observation of the topological soliton state in the Su–Schrieffer–Heeger model, Nat. Commun., Volume 7 (2016)
[230] Direct observation of chiral currents and magnetic reflection in atomic flux lattices, Sci. Adv., Volume 3 (2017) no. 4
[231] Flux-dependent localisation in a disordered flat-band lattice | arXiv
[232] Synthetic dimensions for cold atoms from shaking a harmonic trap, Phys. Rev. A, Volume 95 (2017) no. 2
[233] Different lattice geometries with a synthetic dimension, Phys. Rev. A, Volume 94 (2016)
[234] Quantum simulation of non-trivial topology, New J. Phys., Volume 17 (2015) no. 4
[235] Quantum simulation of 2D topological physics in a 1D array of optical cavities, Nat. Commun., Volume 6 (2015), p. 8704
[236] Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics, Phys. Rev. A, Volume 93 (2016) no. 4
[237] Photonic gauge potential in a system with a synthetic frequency dimension, Opt. Lett., Volume 41 (2016) no. 4, pp. 741-744
[238] Optomechanical creation of magnetic fields for photons on a lattice, Optica, Volume 2 (2015) no. 7, pp. 635-641
[239] Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett., Volume 61 (1988), pp. 2015-2018
[240] The electronic properties of graphene, Rev. Mod. Phys., Volume 81 (2009) no. 1, p. 109
[241] Chern–Simons terms and n field in haldane's model for the quantum Hall effect without landau levels, Phys. Rev. Lett., Volume 65 (1990) no. 2, p. 251
[242] Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Phys. Rev. B, Volume 74 (2006) no. 8
[243] Measuring topology in a laser-coupled honeycomb lattice: from Chern insulators to topological semi-metals, New J. Phys., Volume 15 (2013) no. 1
[244] Quantum anomalous Hall effect in graphene from rashba and exchange effects, Phys. Rev. B, Volume 82 (2010) no. 16
[245] Topological phases in a two-dimensional lattice: magnetic field versus spin–orbit coupling, Phys. Rev. B, Volume 86 (2012) no. 7
[246] Microscopic theory of quantum anomalous Hall effect in graphene, Phys. Rev. B, Volume 85 (2012) no. 11
[247] et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science, Volume 340 (2013) no. 6129, pp. 167-170
[248] Discrete optics in femtosecond-laser-written photonic structures, J. Phys. B, At. Mol. Opt. Phys., Volume 43 (2010) no. 16
[249] et al. Experimental Simulation of Solid-State Phenomena Using Photonic Lattices, Heriot-Watt University, Edinburgh, UK, 2016 (PhD thesis)
[250] et al. Observation of unconventional edge states in ‘photonic graphene’, Nat. Mater., Volume 13 (2014) no. 1, pp. 57-62
[251] Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice, Nat. Commun., Volume 8 (2017)
[252] Observation of photonic anomalous Floquet topological insulators, Nat. Commun., Volume 8 (2017)
[253] Anomalous edge states and the bulk–edge correspondence for periodically driven two-dimensional systems, Phys. Rev. X, Volume 3 (2013) no. 3
[254] Topological singularities and the general classification of Floquet Bloch systems, New J. Phys., Volume 17 (2015) no. 12, pp. 1-22
[255] Quantum simulation of frustrated classical magnetism in triangular optical lattices, Science, Volume 333 (2011) no. 6045, pp. 996-999
[256] Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields, Nat. Phys., Volume 9 (2013), pp. 738-743 | arXiv
[257] Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice, Europhys. Lett., Volume 89 (2010) no. 1
[258] Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature, Volume 483 (2012) no. 7389, pp. 302-305
[259] Floquet topological states in shaking optical lattices, Phys. Rev. A, Volume 89 (2014) no. 6
[260] Hall effect in ferromagnetics, Phys. Rev., Volume 95 (1954) no. 5, p. 1154
[261] Observation of dynamical vortices after quenches in a system with topology, Nat. Phys., Volume 14 (2018), pp. 265-268
[262] Characterizing topology by dynamics: Chern number from linking number | arXiv
[263] Scheme to measure the topological number of a Chern insulator from quench dynamics, Phys. Rev. Lett., Volume 118 (2017)
[264] Experimental reconstruction of the Berry curvature in a Floquet Bloch band, Science, Volume 352 (2016) no. 6289, pp. 1091-1094
[265] Electric field effect in atomically thin carbon films, Science, Volume 306 (2004) no. 5696, pp. 666-669
[266] Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics, J. Phys. Chem. B, Volume 108 (2004) no. 52, pp. 19912-19916
[267] Two-dimensional gas of massless Dirac fermions in graphene, Nature, Volume 438 (2005) no. 7065, pp. 197-200
[268] The rise of graphene, Nat. Mater., Volume 6 (2007) no. 3, pp. 183-191
[269] Graphene: carbon in two dimensions, Mater. Today, Volume 10 (2007) no. 1–2, pp. 20-27
[270] Exploring graphene Recent research advances, Solid State Commun., Volume 143 (2007) no. 1–2, pp. 1-126
[271] Graphene: status and prospects, Science, Volume 324 (2009) no. 5934, pp. 1530-1534
[272] Imaging active topological defects in carbon nanotubes, Nature, Volume 2 (2007) no. 6, pp. 358-360
[273] Theoretical studies of icosahedral C 60 and some related species, Chem. Phys. Lett., Volume 128 (1986) no. 5–6, pp. 501-503
[274] Dislocations in graphene, New J. Phys., Volume 10 (2008) no. 5
[275] Magnetic moments in the presence of topological defects in graphene, Phys. Rev. B, Volume 79 (2009) no. 7
[276] Graphene cones: classification by fictitious flux and electronic properties, Phys. Rev. B, Volume 69 (2004) no. 3
[277] Geometric phases in graphitic cones, Phys. Lett. A, Volume 372 (2008) no. 32, pp. 5368-5371
[278] Electronic properties of curved carbon nanostructures, Rom. J. Phys., Volume 50 (2005) no. 3–4, pp. 435-442
[279] Charge inhomogeneities due to smooth ripples in graphene sheets, Phys. Rev. B, Volume 76 (2007) no. 16
[280] The structure of suspended graphene sheets, Nature, Volume 446 (2007), pp. 60-63
[281] On the roughness of single- and bi-layer graphene membranes, Solid State Commun., Volume 143 (2007) no. 1–2, pp. 101-109
[282] High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface, Proc. Natl. Acad. Sci. USA, Volume 104 (2007) no. 22, pp. 9209-9212
[283] Atomic structure of graphene on SiO2, Nano Lett., Volume 7 (2007) no. 6, pp. 1643-1648
[284] On the geometrical and physical foundations of the theory of yielding, Proceedings of the 2nd Japan National Congress for Applied Mechanics, 1952, p. 41
[285] Gauge Fields in Condensed Matter, vols. 1 and 2, World Scientific, Singapore, 1989
[286] Theory of defects in solids and three-dimensional gravity, Ann. Phys., Volume 216 (1992), p. 1
[287] Dislocations and torsion in graphene and related systems, Nucl. Phys. B, Volume 828 (2010), p. 625
[288] Size, shape, and low energy electronic structure of carbon nanotubes, Phys. Rev. Lett., Volume 78 (1997) no. 10, pp. 1932-1935
[289] Graphene: new bridge between condensed matter physics and quantum electrodynamics, Solid State Commun., Volume 143 (2007) no. 1–2, pp. 3-13
[290] Midgap states and charge inhomogeneities in corrugated graphene, Phys. Rev. B, Volume 77 (2008) no. 7
[291] Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering, Nat. Phys., Volume 6 (2010) no. 1, pp. 30-33
[292] Generating quantizing pseudomagnetic fields by bending graphene ribbons, Phys. Rev. B, Volume 81 (2010) no. 3
[293] Aharonov–Bohm interferences from local deformations in graphene, Nat. Phys., Volume 7 (2011), pp. 810-815
[294] Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles, Science, Volume 329 (2010) no. 5991, pp. 544-547
[295] Propagating edge states in strained honeycomb lattices, Phys. Rev. B, Volume 95 (2017) no. 24
[296] Artificial honeycomb lattices for electrons, atoms and photons, Nat. Nanotechnol., Volume 8 (2013), pp. 625-633
[297] Designer Dirac fermions and topological phases in molecular graphene, Nature, Volume 483 (2012) no. 7389, pp. 306-310
[298] Non-Abelian gauge fields through density wave order and strain in graphene, Phys. Rev. B, Volume 86 (2012) no. 8
[299] Non-Abelian gauge fields and quadratic band touching in molecular graphene, Phys. Rev. B, Volume 87 (2013) no. 12
[300] Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations, 2D Mater., Volume 5 (2018) no. 2
[301] Elastic gauge fields in Weyl semimetals, Phys. Rev. Lett., Volume 115 (2015) no. 17
[302] Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures, Nat. Photonics, Volume 7 (2013) no. 2, pp. 153-158
[303] Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices, Phys. Rev. Lett., Volume 110 (2013) no. 1
[304] Landau levels in strained optical lattices, Phys. Rev. Lett., Volume 115 (2015) no. 23
[305] Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials, Phys. Rev. Lett., Volume 119 (2017)
[306] Strain-induced gauge field and Landau levels in acoustic structures, Phys. Rev. Lett., Volume 118 (2017) no. 19
[307] Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, Springer Tracts Mod. Phys., vol. 191, Springer, Berlin, New York, 2003
[308] Observation of the spin Hall effect in semiconductors, Science, Volume 306 (2004) no. 5703, pp. 1910-1913
[309] Quantum spin Hall insulator state in HgTe quantum wells, Science, Volume 318 (2007) no. 5851, p. 766
[310] The emergence of spin electronics in data storage, Nat. Mater., Volume 6 (2007) no. 11, pp. 813-823
[311] Z 2 topological order and the quantum spin Hall effect, Phys. Rev. Lett., Volume 95 (2005) no. 14
[312] Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science, Volume 314 (2006) no. 5806, p. 1757
[313] A topological Dirac insulator in a quantum spin Hall phase, Nature, Volume 452 (2008) no. 7190, pp. 970-974
[314] Theory of the effect of spin–orbit coupling on magnetic resonance in some semiconductors, Phys. Rev., Volume 96 (1954) no. 2, p. 266
[315] Quantum Theory of Solids, vol. 3, Wiley, New York, 1963
[316] Spin–orbit coupling effects in zinc blende structures, Phys. Rev., Volume 100 (1955) no. 2, p. 580
[317] Quantized surface states of a narrow-gap semiconductor, J. Phys. Soc. Jpn., Volume 37 (1974) no. 5, pp. 1325-1333
[318] Properties of semiconductors with an extremum loop. I. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop, Phys. Solid State, Volume 2 (1960), pp. 1109-1122
[319] Oscillatory effects and the magnetic susceptibility of carriers in inversion layers, J. Phys. C, Solid State Phys., Volume 17 (1984) no. 33, p. 6039
[320] New perspectives for rashba spin–orbit coupling, Nat. Mater., Volume 14 (2015) no. 9, pp. 871-882
[321] Gate control of spin–orbit interaction in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure, Phys. Rev. Lett., Volume 78 (1997) no. 7, p. 1335
[322] Experimental separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells, Phys. Rev. Lett., Volume 92 (2004) no. 25
[323] Measurement of Rashba and Dresselhaus spin–orbit magnetic fields, Nat. Phys., Volume 3 (2007) no. 9
[324] Large rashba splitting in inas quantum wells due to electron wave function penetration into the barrier layers, Phys. Rev. Lett., Volume 84 (2000) no. 26, p. 6074
[325] Spin–orbit interaction in a two-dimensional electron gas in a inas/alsb quantum well with gate-controlled electron density, Phys. Rev. B, Volume 57 (1998) no. 19
[326] Rashba spin splitting in inversion layers on p-type bulk InAs, Phys. Rev. B, Volume 61 (2000) no. 23
[327] Electronic analog of the electro-optic modulator, Appl. Phys. Lett., Volume 56 (1990) no. 7, pp. 665-667
[328] Nonballistic spin-field-effect transistor, Phys. Rev. Lett., Volume 90 (2003) no. 14
[329] Experimental demonstration of spin geometric phase: radius dependence of time-reversal aharonov-casher oscillations, Phys. Rev. Lett., Volume 108 (2012) no. 8
[330] Control of the spin geometric phase in semiconductor quantum rings, Nat. Commun., Volume 4 (2013), p. 2526
[331] Progress, challenges, and opportunities in two-dimensional materials beyond graphene, ACS Nano, Volume 7 (2013) no. 4, pp. 2898-2926
[332] Graphene-like two-dimensional materials, Chem. Rev., Volume 113 (2013) no. 5, pp. 3766-3798
[333] Topological phases in two-dimensional materials: a review, Rep. Prog. Phys., Volume 79 (2016) no. 6
[334] Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks, Phys. Scr., Volume 2015 (2015) no. T164
[335] Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys., Volume 90 (2018)
[336] Theory of the edge states in fractional quantum Hall effects, Int. J. Mod. Phys. B, Volume 6 (1992) no. 10, pp. 1711-1762
[337] The translational side of topological band insulators, J. Phys. Chem. Solids (2018) (available online 31 January 2018)
[338] Quantum spin Hall effect in graphene, Phys. Rev. Lett., Volume 95 (2005) no. 22
[339] Tight-binding approach to uniaxial strain in graphene, Phys. Rev. B, Volume 80 (2009) no. 4
[340] Engineering a robust quantum spin Hall state in graphene via adatom deposition, Phys. Rev. X, Volume 1 (2011) no. 2
[341] Colossal enhancement of spin–orbit coupling in weakly hydrogenated graphene, Nat. Phys., Volume 9 (2013) no. 5, p. 284
[342] et al. Giant spin Hall effect in graphene grown by chemical vapour deposition, Nat. Commun., Volume 5 (2014), p. 4748
[343] Giant Rashba splitting in graphene due to hybridization with gold, Nat. Commun., Volume 3 (2012), p. 1232
[344] et al. Spatial variation of a giant spin–orbit effect induces electron confinement in graphene on Pb islands, Nat. Phys., Volume 11 (2015) no. 1, p. 43
[345] et al. Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state, Nature, Volume 505 (2014) no. 7484, p. 528
[346] et al. Spin–orbit proximity effect in graphene, Nat. Commun., Volume 5 (2014), p. 4875
[347] Quantum spin Hall effect in silicene and two-dimensional germanium, Phys. Rev. Lett., Volume 107 (2011) no. 7
[348] Tunable bandgap in silicene and germanene, Nano Lett., Volume 12 (2011) no. 1, pp. 113-118
[349] Silicene: compelling experimental evidence for graphenelike two-dimensional silicon, Phys. Rev. Lett., Volume 108 (2012) no. 15
[350] Germanene: a novel two-dimensional germanium allotrope akin to graphene and silicene, New J. Phys., Volume 16 (2014) no. 9
[351] Large-gap quantum spin Hall insulators in tin films, Phys. Rev. Lett., Volume 111 (2013) no. 13
[352] Epitaxial growth of two-dimensional stanene, Nat. Mater., Volume 14 (2015) no. 10, pp. 1020-1025
[353] Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol., Volume 7 (2012) no. 11, pp. 699-712
[354] Quantum spin Hall effect in two-dimensional crystals of transition-metal dichalcogenides, Phys. Rev. Lett., Volume 113 (2014) no. 7
[355] Quantum spin Hall effect in two-dimensional transition metal dichalcogenides, Science, Volume 346 (2014) no. 6215, pp. 1344-1347
[356] Effect of induced spin–orbit coupling for atoms via laser fields, Phys. Rev. Lett., Volume 102 (2009) no. 4
[357] Spin–orbit-coupled Bose–Einstein condensates, Nature, Volume 471 (2011) no. 7336, pp. 83-86
[358] Spin-injection spectroscopy of a spin–orbit coupled Fermi gas, Phys. Rev. Lett., Volume 109 (2012) no. 9
[359] Spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett., Volume 109 (2012) no. 9
[360] Long-lived spin–orbit coupled degenerate dipolar Fermi gas, Phys. Rev. X, Volume 6 (2016) no. 3
[361] Spin-orbit-coupled two-electron Fermi gases of ytterbium atoms, Phys. Rev. A, Volume 94 (2016) 061604(R)
[362] Tunable spin–orbit coupling via strong driving in ultracold-atom systems, Phys. Rev. Lett., Volume 114 (2015) no. 12
[363] Realizing one-dimensional topological superfluids with ultracold atomic gases, J. Phys. B, At. Mol. Opt. Phys., Volume 46 (2013) no. 13
[364] Synthetic gauge field with highly magnetic lanthanide atoms, Phys. Rev. A, Volume 88 (2013) no. 1
[365] Chiral ladders and the edges of quantum Hall insulators, Phys. Rev. A, Volume 89 (2014) no. 2
[366] Tunneling-assisted spin–orbit coupling in bilayer Bose–Einstein condensates, Phys. Rev. A, Volume 91 (2015) no. 3
[367] Spin–orbit coupled spinor Bose–Einstein condensates, Phys. Rev. Lett., Volume 105 (2010) no. 16
[368] Raman-dressed spin-1 spin–orbit coupled quantum gas, Phys. Rev. A, Volume 89 (2014) no. 2
[369] Striped ferronematic ground states in a spin–orbit coupled bose gas, Phys. Rev. A, Volume 91 (2015) no. 2
[370] Magnetic phases of spin-1 spin–orbit coupled bose gases, Nat. Commun., Volume 7 (2016)
[371] Laser-driven population transfer in four-level atoms: consequences of non-Abelian geometrical adiabatic phase factors, Phys. Rev. A, Volume 59 (1999) no. 4, p. 2910
[372] Non-Abelian gauge potentials for ultracold atoms with degenerate dark states, Phys. Rev. Lett., Volume 95 (2005) no. 1
[373] Generalized Rashba–Dresselhaus spin–orbit coupling for cold atoms, Phys. Rev. A, Volume 81 (2010) no. 5
[374] Realistic Rashba and Dresselhaus spin–orbit coupling for neutral atoms, Phys. Rev. A, Volume 84 (2011) no. 2
[375] Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases, Nat. Phys., Volume 12 (2016)
[376] Experimental observation of a topological band gap opening in ultracold Fermi gases with two-dimensional, spin–orbit coupling, Phys. Rev. Lett., Volume 117 (2016) no. 23
[377] Realization of two-dimensional spin–orbit coupling for Bose–Einstein condensates, Science, Volume 354 (2016) no. 6308
[378] Detecting topological phases in cold atoms, Phys. Rev. Lett., Volume 111 (2013) no. 12
[379] Wilson fermions and axion electrodynamics in optical lattices, Phys. Rev. Lett., Volume 105 (2010) no. 19
[380] Synthetic 3d spin–orbit coupling, Phys. Rev. Lett., Volume 108 (2012) no. 23
[381] An optical-lattice-based quantum simulator for relativistic field theories and topological insulators, New J. Phys., Volume 14 (2012) no. 1
[382] Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space, Phys. Rev. Lett., Volume 114 (2015) no. 22
[383] Spin–orbit coupling in periodically driven optical lattices, Phys. Rev. A, Volume 90 (2014) no. 3
[384] Spin–orbit coupling and quantum spin Hall effect for neutral atoms without spin flips, Phys. Rev. Lett., Volume 111 (2013) no. 22
[385] Transverse collisional instabilities of a Bose–Einstein condensate in a driven one-dimensional lattice, Phys. Rev. A, Volume 91 (2015) no. 2
[386] Scattering theory for Floquet–Bloch states, Phys. Rev. A, Volume 91 (2015)
[387] Multiphoton interband excitations of quantum gases in driven optical lattices, Phys. Rev. A, Volume 92 (2015) no. 4
[388] Parametric instability rates in periodically driven band systems, Phys. Rev. X, Volume 7 (2017) no. 2
[389] Synthetic spin–orbit coupling in an optical lattice clock, Phys. Rev. Lett., Volume 116 (2016) no. 3
[390] Collective dipole oscillations of a spin–orbit coupled Bose–Einstein condensate, Phys. Rev. Lett., Volume 109 (2012) no. 11
[391] Observation of Zitterbewegung in a spin–orbit coupled Bose–Einstein condensate, Phys. Rev. A, Volume 88 (2013) no. 2
[392] Direct observation of zitterbewegung in a Bose–Einstein condensate, New J. Phys., Volume 15 (2013) no. 7
[393] Spin field effect transistors with ultracold atoms, Phys. Rev. Lett., Volume 101 (2008) no. 26
[394] The spin Hall effect in a quantum gas, Nature, Volume 498 (2013) no. 7453
[395] Tunable Landau–Zener transitions in a spin–orbit coupled Bose–Einstein condensate, Phys. Rev. A, Volume 90 (2014) no. 1
[396] Exotic superfluidity in spin–orbit coupled Bose–Einstein condensates, Europhys. Lett., Volume 100 (2012) no. 5
[397] Spin-orbit-coupled Bose–Einstein condensates in a one-dimensional optical lattice, Phys. Rev. Lett., Volume 114 (2015) no. 7
[398] superfluid from s-wave interactions of fermionic cold atoms, Phys. Rev. Lett., Volume 101 (2008) no. 16
[399] Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field, Phys. Rev. B, Volume 83 (2011) no. 9
[400] Rashba spin–orbit coupled atomic Fermi gases, Phys. Rev. A, Volume 84 (2011) no. 6
[401] Topological superfluid in a trapped two-dimensional polarized Fermi gas with spin–orbit coupling, Phys. Rev. A, Volume 84 (2011) no. 6
[402] Synthetic partial waves in ultracold atomic collisions, Science, Volume 335 (2012) no. 6066, pp. 314-317
[403] Raman-induced interactions in a single-component Fermi gas near an s-wave Feshbach resonance, Phys. Rev. Lett., Volume 111 (2013) no. 9
[404] Production of Feshbach molecules induced by spin–orbit coupling in Fermi gases, Nat. Phys., Volume 10 (2014) no. 2, pp. 110-115
[405] Radio-frequency spectroscopy of a strongly interacting spin–orbit coupled Fermi gas, Phys. Rev. A, Volume 87 (2013) no. 5
[406] Experimental determination of the finite-temperature phase diagram of a spin–orbit coupled Bose gas, Nat. Phys., Volume 10 (2014) no. 4
[407] Bose–Einstein condensates with spin–orbit interaction, Phys. Rev. Lett., Volume 107 (2011) no. 15
[408] Quantum tricriticality and phase transitions in spin–orbit coupled Bose–Einstein condensates, Phys. Rev. Lett., Volume 108 (2012) no. 22
[409] Dicke-type phase transition in a spin–orbit coupled Bose–Einstein condensate, Nat. Commun., Volume 5 (2014)
[410] Softening of roton and phonon modes in a Bose–Einstein condensate with spin–orbit coupling, Phys. Rev. Lett., Volume 114 (2015) no. 10
[411] A stripe phase with supersolid properties in spin–orbit coupled Bose–Einstein condensates, Nature, Volume 543 (2017) no. 7643, pp. 91-94
[412] Unpaired Majorana fermions in quantum wires, Phys. Usp., Volume 44 (2001) no. 10S, p. 131
[413] Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms, Phys. Rev. Lett., Volume 103 (2009) no. 2
[414] Majorana fermions in equilibrium and in driven cold-atom quantum wires, Phys. Rev. Lett., Volume 106 (2011) no. 22
[415] Probing non-Abelian statistics of majorana fermions in ultracold atomic superfluid, Phys. Rev. Lett., Volume 106 (2011) no. 10
[416] Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B, Volume 83 (2011) no. 20
[417] Tunable topological Weyl semimetal from simple-cubic lattices with staggered fluxes, Phys. Rev. A, Volume 85 (2012) no. 3
[418] Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice, Phys. Rev. A, Volume 92 (2015) no. 1
[419] Realization and detection of Weyl semimetals and the chiral anomaly in cold atomic systems, Phys. Rev. A, Volume 94 (2016) no. 1
[420] Spin–orbit coupled quantum gases, Int. J. Mod. Phys. B, Volume 26 (2012) no. 01
[421] Unconventional states of bosons with the synthetic spin–orbit coupling, J. Phys. B, At. Mol. Opt. Phys., Volume 46 (2013) no. 13
[422] Spin–orbit coupling in quantum gases, Nature, Volume 494 (2013) no. 7435
[423] Spin–orbit interaction of a photon in an inhomogeneous medium, Phys. Rev. A, Volume 46 (1992) no. 8, p. 5199
[424] Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect, Phys. Rev. E, Volume 70 (2004) no. 2
[425] Spin–orbit interactions of light, Nat. Photonics, Volume 9 (2015) no. 12, pp. 796-808
[426] On the transition from wave to geometrical optics, Dokl. Akad. Nauk SSSR, Volume 18 (1938), pp. 263-267
[427] On the plane polarization in a curvilinear light ray, Dokl. Acad. Nauk USSR, Volume 31 (1940), p. 222
[428] Manifestations of Berry's topological phase for the photon, Phys. Rev. Lett., Volume 57 (1986) no. 8, p. 933
[429] Observation of Berry's topological phase by use of an optical fiber, Phys. Rev. Lett., Volume 57 (1986) no. 8, p. 937
[430] Hall effect of light, Phys. Rev. Lett., Volume 93 (2004) no. 8
[431] Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet, Phys. Rev. Lett., Volume 96 (2006) no. 7
[432] Ein neuer und fundamentaler versuch zur totalreflexion, Ann. Phys., Volume 436 (1947) no. 7–8, pp. 333-346
[433] K teorii polnogo otrazheniya, Dokl. Akad. Nauk SSSR, Volume 105 (1955) no. 3, pp. 465-468
[434] Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam, Phys. Rev. D, Volume 5 (1972) no. 4, p. 787
[435] Goos–Hänchen and Imbert–Fedorov beam shifts: an overview, J. Opt., Volume 15 (2013) no. 1
[436] Experimental observation of the Imbert–Fedorov transverse displacement after a single total reflection, Appl. Opt., Volume 43 (2004) no. 9, pp. 1863-1869
[437] Observation of the spin Hall effect of light via weak measurements, Science, Volume 319 (2008) no. 5864, pp. 787-790
[438] Measurement of spin Hall effect of reflected light, Opt. Lett., Volume 34 (2009) no. 17, pp. 2551-2553
[439] Geometrodynamics of spinning light, Nat. Photonics, Volume 2 (2008) no. 12, pp. 748-753
[440] Spin Hall effect of reflected light at the air-uniaxial crystal interface, Opt. Express, Volume 18 (2010) no. 16, pp. 16832-16839
[441] Ultrafast optical imaging of the spin Hall effect of light in semiconductors, Phys. Rev. B, Volume 82 (2010) no. 4
[442] Spin Hall effect of light in metallic reflection, Opt. Lett., Volume 36 (2011) no. 16, pp. 3200-3202
[443] Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements, Phys. Rev. A, Volume 85 (2012) no. 4
[444] Identifying graphene layers via spin Hall effect of light, Appl. Phys. Lett., Volume 101 (2012) no. 25
[445] Photonic spin Hall effect at metasurfaces, Science, Volume 339 (2013) no. 6126, pp. 1405-1407
[446] Spin-to-orbital angular momentum conversion in a strongly focused optical beam, Phys. Rev. Lett., Volume 99 (2007) no. 7
[447] Spin Hall effect of light in spherical geometry, Phys. Rev. Lett., Volume 102 (2009) no. 12
[448] Optical nanoprobing via spin–orbit interaction of light, Phys. Rev. Lett., Volume 104 (2010) no. 25
[449] Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications, J. Opt., Volume 13 (2011) no. 6
[450] Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light, Nano Lett., Volume 13 (2013) no. 9, pp. 4148-4151
[451] Transverse shift of a focal spot due to switching of the sign of circular polarization, JETP Lett., Volume 59 (1994) no. 4, pp. 232-234
[452] Coriolis effect in optics: unified geometric phase and spin-Hall effect, Phys. Rev. Lett., Volume 101 (2008) no. 3
[453] Observation of the spin-based plasmonic effect in nanoscale structures, Phys. Rev. Lett., Volume 101 (2008) no. 4
[454] Optical spin Hall effects in plasmonic chains, Nano Lett., Volume 11 (2011) no. 5, pp. 2038-2042
[455] Weak measurements of light chirality with a plasmonic slit, Phys. Rev. Lett., Volume 109 (2012) no. 1
[456] Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect, Appl. Phys. Lett., Volume 105 (2014) no. 15
[457] Spin-polarized photon emission by resonant multipolar nanoantennas, ACS Photonics, Volume 1 (2014) no. 11, pp. 1218-1223
[458] Polarization-controlled tunable directional coupling of surface plasmon polaritons, Science, Volume 340 (2013) no. 6130, pp. 331-334
[459] Spin-optical metamaterial route to spin-controlled photonics, Science, Volume 340 (2013) no. 6133, pp. 724-726
[460] Plasmonic meta-atoms and metasurfaces, Nat. Photonics, Volume 8 (2014) no. 12, pp. 889-898
[461] Spin–orbit coupling in surface plasmon scattering by nanostructures, Nat. Commun., Volume 5 (2014), p. 5327
[462] Photonic spin Hall effect in metasurfaces: a brief review, Nanophotonics, Volume 6 (2017) no. 1, pp. 51-70
[463] Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media, Phys. Rev. Lett., Volume 96 (2006) no. 16
[464] Quantum information transfer from spin to orbital angular momentum of photons, Phys. Rev. Lett., Volume 103 (2009) no. 1
[465] Optical vortices from liquid crystal droplets, Phys. Rev. Lett., Volume 103 (2009) no. 10
[466] Electrically controlled topological defects in liquid crystals as tunable spin–orbit encoders for photons, Opt. Lett., Volume 36 (2011) no. 5, pp. 719-721
[467] et al. Principles of Optics, Pergamon Press, 1980
[468] Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A, Volume 35 (1971) no. 6, pp. 459-460
[469] Exchange interaction in excitons in semiconductors, Sov. Phys. JETP, Volume 33 (1971), p. 108
[470] Exciton spin dynamics in quantum wells, Phys. Rev. B, Volume 47 (1993) no. 23
[471] Optical spin Hall effect, Phys. Rev. Lett., Volume 95 (2005) no. 13
[472] Observation of the optical spin Hall effect, Nat. Phys., Volume 3 (2007) no. 9, p. 628
[473] Polariton polarization-sensitive phenomena in planar semiconductor microcavities, Semicond. Sci. Technol., Volume 25 (2009) no. 1
[474] et al. Spin–orbit coupling for photons and polaritons in microstructures, Phys. Rev. X, Volume 5 (2015) no. 1
[475] Strong and weak coupling regime in pillar semiconductor microcavities, Physica E, Low-Dimens. Syst. Nanostruct., Volume 2 (1998) no. 1, pp. 915-919
[476] Spin–orbit coupling and the optical spin Hall effect in photonic graphene, Phys. Rev. Lett., Volume 114 (2015) no. 2
[477] Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons, Phys. Rev. Lett., Volume 112 (2014) no. 11
[478] Non-Abelian gauge fields in photonic cavities and photonic superfluids, Phys. Rev. Lett., Volume 112 (2014) no. 6
[479] Two-dimensional topological photonic systems, Prog. Quantum Electron., Volume 55 (2017), pp. 52-73
[480] et al. Probing topological protection using a designer surface plasmon structure, Nat. Commun., Volume 7 (2016)
[481] Photonic topological insulators, Nat. Mater., Volume 12 (2013) no. 3, pp. 233-239
[482] Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide, Nat. Commun., Volume 5 (2014), p. 5782
[483] Robust reconfigurable electromagnetic pathways within a photonic topological insulator, Nat. Mater., Volume 15 (2016) no. 5, pp. 542-548
[484] Experimental demonstration of topological effects in bianisotropic metamaterials, Sci. Rep., Volume 6 (2016)
[485] Weyl points and line nodes in gyroid photonic crystals, Nat. Photonics, Volume 7 (2013) no. 4, pp. 294-299
[486] Experimental observation of Weyl points, Science, Volume 349 (2015) no. 6248, pp. 622-624
[487] Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states, Nat. Commun., Volume 7 (2016)
[488] Topological phases of sound and light, Phys. Rev. X, Volume 5 (2015)
[489] Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice, Nat. Commun., Volume 6 (2015), p. 8260
[490] Manipulation of Dirac cones in mechanical graphene, Sci. Rep., Volume 5 (2015)
[491] Pseudomagnetic fields for sound at the nanoscale, Proc. Natl. Acad. Sci., Volume 114 (2017) no. 17, p. E3390-E3395
[492] Acoustic metamaterials: from local resonances to broad horizons, Sci. Adv., Volume 2 (2016) no. 2
[493] Spin–orbit coupling in a hexagonal ring of pendula, New J. Phys., Volume 19 (2017)
[494] Surface phononic graphene, Nat. Mater., Volume 15 (2016) no. 12, pp. 1243-1247
[495] Observation of acoustic valley vortex states and valley-chirality locked beam splitting, Phys. Rev. B, Volume 95 (2017) no. 17
[496] Experimental demonstration of topologically protected efficient sound propagation in an acoustic waveguide network, Phys. Rev. B, Volume 95 (2017) no. 9
[497] Topological phononic insulator with robustly pseudospin-dependent transport, Phys. Rev. B, Volume 96 (2017)
[498] Two applications of axion electrodynamics, Phys. Rev. Lett., Volume 58 (1987) no. 18, p. 1799
[499] It's been a Weyl coming, Nat. Phys., Volume 11 (2015), pp. 698-699
[500] Anomalies in Quantum Field Theory, vol. 91, Oxford University Press, 2000
[501] Colloquium: majorana fermions in nuclear, particle, and solid-state physics, Rev. Mod. Phys., Volume 87 (2015), pp. 137-163
[502] Cold atom simulation of interacting relativistic quantum field theories, Phys. Rev. Lett., Volume 105 (2010)
[503] Simulating compact quantum electrodynamics with ultracold atoms: probing confinement and nonperturbative effects, Phys. Rev. Lett., Volume 109 (2012)
[504] Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench, Phys. Rev. Lett., Volume 109 (2012)
[505] Simulation of non-Abelian gauge theories with optical lattices, Nat. Commun., Volume 4 (2013), p. 2615
[506] Toolbox for Abelian lattice gauge theories with synthetic matter, Phys. Rev. A, Volume 95 (2017)
[507] Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature, Volume 534 (2016) no. 7608, pp. 516-519
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