[1] Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983). doi: 10.1103/PhysRevB.27.6083
[2] Niu, Q. & Thouless, D. J. Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction. J. Phys. A: Math. Gen. 17, 2453–2462 (1984). doi: 10.1088/0305-4470/17/12/016
[3] Kitagawa, T. et al. Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010). doi: 10.1103/PhysRevB.82.235114
[4] Xiao, D., Chang, M. C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010). doi: 10.1103/RevModPhys.82.1959
[5] Haldane, F. D. M. Model for a quantum hall effect without landau levels: condensed-matter realization of the "parity anomaly". Phys. Rev. Lett. 61, 2015–2018 (1988). doi: 10.1103/PhysRevLett.61.2015
[6] Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). doi: 10.1103/RevModPhys.82.3045
[7] Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019). doi: 10.1103/RevModPhys.91.015006
[8] Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008). doi: 10.1103/PhysRevLett.100.013904
[9] Wang, Z. et al. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009). doi: 10.1038/nature08293
[10] Umucalılar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011). doi: 10.1103/PhysRevA.84.043804
[11] Hafezi, M. et al. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011). doi: 10.1038/nphys2063
[12] Fang, K. J., Yu, Z. F. & Fan, S. H. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photonics 6, 782–787 (2012). doi: 10.1038/nphoton.2012.236
[13] Kraus, Y. E. et al. Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett. 109, 106402 (2012). doi: 10.1103/PhysRevLett.109.106402
[14] Kitagawa, T. et al. Observation of topologically protected bound states in photonic quantum walks. Nat. Commun. 3, 882 (2012). doi: 10.1038/ncomms1872
[15] Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013). doi: 10.1038/nature12066
[16] Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2013). doi: 10.1038/nmat3520
[17] Hafezi, M. et al. Imaging topological edge states in silicon photonics. Nat. Photonics 7, 1001–1005 (2013). doi: 10.1038/nphoton.2013.274
[18] Hau, L. V. et al. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 397, 594–598 (1999). doi: 10.1038/17561
[19] Harris, S. E. & Hau, L. V. Nonlinear optics at low light levels. Phys. Rev. Lett. 82, 4611–4614 (1999). doi: 10.1103/PhysRevLett.82.4611
[20] Yariv, A. et al. Coupled-resonator optical waveguide: a proposal and analysis. Opt. Lett. 24, 711–713 (1999). doi: 10.1364/OL.24.000711
[21] Ku, P. C. et al. Slow light in semiconductor quantum wells. Opt. Lett. 29, 2291–2293 (2004). doi: 10.1364/OL.29.002291
[22] Vlasov, Y. A. et al. Active control of slow light on a chip with photonic crystal waveguides. Nature 438, 65–69 (2005). doi: 10.1038/nature04210
[23] Hughes, S. et al. Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity. Phys. Rev. Lett. 94, 033903 (2005). doi: 10.1103/PhysRevLett.94.033903
[24] Povinelli, M. L., Johnson, S. G. & Joannopoulos, J. D. Slow-light, band-edge waveguides for tunable time delays. Opt. Express 13, 7145–7159 (2005). doi: 10.1364/OPEX.13.007145
[25] Baba, T. Slow light in photonic crystals. Nat. Photonics 2, 465–473 (2008). doi: 10.1038/nphoton.2008.146
[26] Hao, R. et al. Novel slow light waveguide with controllable delay-bandwidth product and utra-low dispersion. Opt. Express 18, 5942–5950 (2010). doi: 10.1364/OE.18.005942
[27] Minkov, M. & Fan, S. H. Unidirectional light transport in dynamically modulated waveguides. Phys. Rev. Appl. 10, 044028 (2018). doi: 10.1103/PhysRevApplied.10.044028
[28] Guglielmon, J. & Rechtsman, M. C. Broadband topological slow light through higher momentum-space winding. Phys. Rev. Lett. 122, 153904 (2019). doi: 10.1103/PhysRevLett.122.153904
[29] Thouless, D. J. et al. Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982). doi: 10.1103/PhysRevLett.49.405
[30] Verbin, M. et al. Topological pumping over a photonic Fibonacci quasicrystal. Phys. Rev. B 91, 064201 (2015). doi: 10.1103/PhysRevB.91.064201
[31] Zilberberg, O. et al. Photonic topological boundary pumping as a probe of 4d quantum Hall physics. Nature 553, 59–62 (2018). doi: 10.1038/nature25011
[32] Grinberg, I. H. et al. Robust temporal pumping in a magneto-mechanical topological insulator. Nat. Commun. 11, 974 (2020). doi: 10.1038/s41467-020-14804-0
[33] Khemani, V., Nandkishore, R. & Sondhi, S. L. Nonlocal adiabatic response of a localized system to local manipulations. Nat. Phys. 11, 560–565 (2015). doi: 10.1038/nphys3344
[34] Zhou, L. W., Tan, D. Y. & Gong, J. B. Effects of dephasing on quantum adiabatic pumping with nonequilibrium initial states. Phys. Rev. B 92, 245409 (2015). doi: 10.1103/PhysRevB.92.245409
[35] Wang, H. L., Zhou, L. W. & Gong, J. B. Interband coherence induced correction to adiabatic pumping in periodically driven systems. Phys. Rev. B 91, 085420 (2015). doi: 10.1103/PhysRevB.91.085420
[36] Privitera, L. et al. Nonadiabatic breaking of topological pumping. Phys. Rev. Lett. 120, 106601 (2018). doi: 10.1103/PhysRevLett.120.106601
[37] Lohse, M. et al. A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice. Nat. Phys. 12, 350–354 (2016). doi: 10.1038/nphys3584
[38] Nakajima, S. et al. Topological Thouless pumping of ultracold fermions. Nat. Phys. 12, 296–300 (2016). doi: 10.1038/nphys3622
[39] Kuno, Y. Disorder-induced Chern insulator in the Harper-Hofstadter-Hatsugai model. Phys. Rev. B 100, 054108 (2019). doi: 10.1103/PhysRevB.100.054108
[40] Ippoliti, M. & Bhatt, R. N. Dimensional crossover of the integer quantum hall plateau transition and disordered topological pumping. Phys. Rev. Lett. 124, 086602 (2020). doi: 10.1103/PhysRevLett.124.086602
[41] Szameit, A. & Nolte, S. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B: At., Mol. Optical Phys. 43, 163001 (2010). doi: 10.1088/0953-4075/43/16/163001
[42] Rice, M. J. & Mele, E. J. Elementary excitations of a linearly conjugated diatomic polymer. Phys. Rev. Lett. 49, 1455–1459 (1982). doi: 10.1103/PhysRevLett.49.1455
[43] Denisov, S. et al. Periodically driven quantum ratchets: symmetries and resonances. Phys. Rev. A 75, 063424 (2007). doi: 10.1103/PhysRevA.75.063424
[44] Salger, T. et al. Directed transport of atoms in a Hamiltonian quantum ratchet. Science 326, 1241–1243 (2009). doi: 10.1126/science.1179546