P. A. Kalozoumis, G. Theocharis, V. Achilleos, S. Félix, O. Richoux, and V. Pagneux, “Finite-size effects on topological interface states in one-dimensional scattering systems,” Phys. Rev. A 98, 023838 (2018).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

L.-J. Lang, X. Cai, and S. Chen, “Edge states and topological phases in one-dimensional optical superlattices,” Phys. Rev. Lett. 108, 220401 (2012).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, “Optical interface states protected by synthetic weyl points,” Phys. Rev. X 7, 031032 (2017).

M.-L. Chang, M. Xiao, W.-J. Chen, and C. T. Chan, “Multiple weyl points and the sign change of their topological charges in woodpile photonic crystals,” Phys. Rev. B 95, 125136 (2017).

[Crossref]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4, 021017 (2014).

M.-L. Chang, M. Xiao, W.-J. Chen, and C. T. Chan, “Multiple weyl points and the sign change of their topological charges in woodpile photonic crystals,” Phys. Rev. B 95, 125136 (2017).

[Crossref]

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]

L.-J. Lang, X. Cai, and S. Chen, “Edge states and topological phases in one-dimensional optical superlattices,” Phys. Rev. Lett. 108, 220401 (2012).

[Crossref]
[PubMed]

M.-L. Chang, M. Xiao, W.-J. Chen, and C. T. Chan, “Multiple weyl points and the sign change of their topological charges in woodpile photonic crystals,” Phys. Rev. B 95, 125136 (2017).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

L. Pilozzi and C. Conti, “Topological lasing in resonant photonic structures,” Phys. Rev. B 93, 195317 (2016).

[Crossref]

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

K. V. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45, 494–497 (1980).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

M. Ezawa, “Spin valleytronics in silicene: Quantum spin hall–quantum anomalous hall insulators and single-valley semimetals,” Phys. Rev. B 87, 155415 (2013).

[Crossref]

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic weyl point in reciprocal chiral metamaterials,” Phys. Rev. Lett. 117, 057401 (2016).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]

P. A. Kalozoumis, G. Theocharis, V. Achilleos, S. Félix, O. Richoux, and V. Pagneux, “Finite-size effects on topological interface states in one-dimensional scattering systems,” Phys. Rev. A 98, 023838 (2018).

[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7, 294 (2013).

[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

A. V. Poshakinskiy, A. N. Poddubny, and M. Hafezi, “Phase spectroscopy of topological invariants in photonic crystals,” Phys. Rev. A 91, 043830 (2015).

[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).

[Crossref]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).

[Crossref]
[PubMed]

M. Z. Hasan and C. L. Kane, “Colloquium,” Rev. Mod. Phys. 82, 3045–3067 (2010).

[Crossref]

Y. Hatsugai, “Chern number and edge states in the integer quantum hall effect,” Phys. Rev. Lett. 71, 3697–3700 (1993).

[Crossref]
[PubMed]

L.-H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114, 223901 (2015).

[Crossref]
[PubMed]

A. V. Poshakinskiy, A. N. Poddubny, L. Pilozzi, and E. L. Ivchenko, “Radiative topological states in resonant photonic crystals,” Phys. Rev. Lett. 112, 107403 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

Q. Li and X. Jiang, “The connection of topology between systems with different dimensions: 1D Zak phases to 2D chern number, weyl point as the jumping channel for one singularity and nodal line to merge all singularities,” ArXiv, 1810.12550 (2018).

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821 (2014).

[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7, 294 (2013).

[Crossref]

P. A. Kalozoumis, G. Theocharis, V. Achilleos, S. Félix, O. Richoux, and V. Pagneux, “Finite-size effects on topological interface states in one-dimensional scattering systems,” Phys. Rev. A 98, 023838 (2018).

[Crossref]

M. Z. Hasan and C. L. Kane, “Colloquium,” Rev. Mod. Phys. 82, 3045–3067 (2010).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

K. V. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45, 494–497 (1980).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

L.-J. Lang, X. Cai, and S. Chen, “Edge states and topological phases in one-dimensional optical superlattices,” Phys. Rev. Lett. 108, 220401 (2012).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]

Q. Li and X. Jiang, “The connection of topology between systems with different dimensions: 1D Zak phases to 2D chern number, weyl point as the jumping channel for one singularity and nodal line to merge all singularities,” ArXiv, 1810.12550 (2018).

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic weyl point in reciprocal chiral metamaterials,” Phys. Rev. Lett. 117, 057401 (2016).

[Crossref]
[PubMed]

Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, “Optical interface states protected by synthetic weyl points,” Phys. Rev. X 7, 031032 (2017).

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821 (2014).

[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7, 294 (2013).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. A. Kalozoumis, G. Theocharis, V. Achilleos, S. Félix, O. Richoux, and V. Pagneux, “Finite-size effects on topological interface states in one-dimensional scattering systems,” Phys. Rev. A 98, 023838 (2018).

[Crossref]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

K. V. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45, 494–497 (1980).

[Crossref]

L. Pilozzi and C. Conti, “Topological lasing in resonant photonic structures,” Phys. Rev. B 93, 195317 (2016).

[Crossref]

A. V. Poshakinskiy, A. N. Poddubny, L. Pilozzi, and E. L. Ivchenko, “Radiative topological states in resonant photonic crystals,” Phys. Rev. Lett. 112, 107403 (2014).

[Crossref]
[PubMed]

A. V. Poshakinskiy, A. N. Poddubny, and M. Hafezi, “Phase spectroscopy of topological invariants in photonic crystals,” Phys. Rev. A 91, 043830 (2015).

[Crossref]

A. V. Poshakinskiy, A. N. Poddubny, L. Pilozzi, and E. L. Ivchenko, “Radiative topological states in resonant photonic crystals,” Phys. Rev. Lett. 112, 107403 (2014).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

A. V. Poshakinskiy, A. N. Poddubny, and M. Hafezi, “Phase spectroscopy of topological invariants in photonic crystals,” Phys. Rev. A 91, 043830 (2015).

[Crossref]

A. V. Poshakinskiy, A. N. Poddubny, L. Pilozzi, and E. L. Ivchenko, “Radiative topological states in resonant photonic crystals,” Phys. Rev. Lett. 112, 107403 (2014).

[Crossref]
[PubMed]

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057–1110 (2011).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100, 013904 (2008).

[Crossref]
[PubMed]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-hall-effect edge states in photonic crystals,” Phys. Rev. A 78, 033834 (2008).

[Crossref]

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

P. A. Kalozoumis, G. Theocharis, V. Achilleos, S. Félix, O. Richoux, and V. Pagneux, “Finite-size effects on topological interface states in one-dimensional scattering systems,” Phys. Rev. A 98, 023838 (2018).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821 (2014).

[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7, 294 (2013).

[Crossref]

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]

P. A. Kalozoumis, G. Theocharis, V. Achilleos, S. Félix, O. Richoux, and V. Pagneux, “Finite-size effects on topological interface states in one-dimensional scattering systems,” Phys. Rev. A 98, 023838 (2018).

[Crossref]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, “Measuring a topological transition in an artificial spin-1/2 system,” Phys. Rev. Lett. 113, 050402 (2014).

[Crossref]
[PubMed]

Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, “Optical interface states protected by synthetic weyl points,” Phys. Rev. X 7, 031032 (2017).

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. O Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, “Observation of topological transitions in interacting quantum circuits,” Nature 515, 241 (2014).

[Crossref]
[PubMed]

L.-H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114, 223901 (2015).

[Crossref]
[PubMed]

Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, “Optical interface states protected by synthetic weyl points,” Phys. Rev. X 7, 031032 (2017).

M.-L. Chang, M. Xiao, W.-J. Chen, and C. T. Chan, “Multiple weyl points and the sign change of their topological charges in woodpile photonic crystals,” Phys. Rev. B 95, 125136 (2017).

[Crossref]

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic weyl point in reciprocal chiral metamaterials,” Phys. Rev. Lett. 117, 057401 (2016).

[Crossref]
[PubMed]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4, 021017 (2014).

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62, 2747–2750 (1989).

[Crossref]
[PubMed]

Z. Gao, Z. Yang, F. Gao, H. Xue, Y. Yang, J. Dong, and B. Zhang, “Valley surface-wave photonic crystal and its bulk/edge transport,” Phys. Rev. B 96, 201402 (2017).

[Crossref]

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057–1110 (2011).

[Crossref]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4, 021017 (2014).

Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, “Optical interface states protected by synthetic weyl points,” Phys. Rev. X 7, 031032 (2017).

W. Zhu, Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, “Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials,” Phys. Rev. B 97, 195307 (2018).

[Crossref]

W. Zhu, X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, “Simultaneous observation of a topological edge state and exceptional point in an open and non-hermitian acoustic system,” Phys. Rev. Lett. 121, 124501 (2018).

[Crossref]
[PubMed]