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Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics.
Solitons in polyacetylene
Su, W., Schrieffer, J. & Heeger, A. J · 1979
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Molding the flow of light (2008)
Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D · 2008
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Phononic crystals and acoustic metamaterials
Lu, M.-H., Feng, L. & Chen, Y.-F · 2009
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Colloquium: Topological insulators
Hasan, M. Z. & Kane, C. L · 2010
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Topological insulators and superconductors
Qi, X.-L. & Zhang, S.-C · 2011
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Topological crystalline insulators
Fu, L · 2011
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Topological insulators in magnetic fields: Quantum hall effect and edge channels with a nonquantized θ \theta term
Sitte, M., Rosch, A., Altman, E. & Fritz, L · 2012
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Observation of topologically protected bound states in photonic quantum walks
Kitagawa, T. et al · 2012
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Surface state magnetization and chiral edge states on topological insulators
Zhang, F., Kane, C. L. & Mele, E. J · 2013
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Floquet topological insulators
Cayssol, J., Dóra, B., Simon, F. & Moessner, R · 2013
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Photonic floquet topological insulators
Rechtsman, M. C. et al · 2013
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Graphene in light: Design, synthesis and applications of photo-active graphene and graphene-like materials
Wang, H.-X., Wang, Q., Zhou, K.-G. & Zhang, H.-L · 2013
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Controlling the spontaneous emission rate of monolayer mos2 in a photonic crystal nanocavity
Gan, X. et al · 2013
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Topological photonics
Lu, L., Joannopoulos, J. D. & Soljačić, M · 2014
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Accidental degeneracy of double dirac cones in a phononic crystal
Chen, Z.-G. et al · 2014
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Two-dimensional material nanophotonics
Xia, F., Wang, H., Xiao, D., Dubey, M. & Ramasubramaniam, A · 2014
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Impurity-bound states and green’s function zeros as local signatures of topology
Slager, R.-J., Rademaker, L., Zaanen, J. & Balents, L · 2015
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Topological acoustics
Yang, Z. et al · 2015
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Geometric phase and band inversion in periodic acoustic systems
Xiao, M. et al · 2015
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Scheme for achieving a topological photonic crystal by using dielectric material
Wu, L.-H. & Hu, X · 2015
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Recent advances in two-dimensional materials beyond graphene
Bhimanapati, G. R. et al · 2015
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Monolayer semiconductor nanocavity lasers with ultralow thresholds
Wu, S. et al · 2015
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Acoustic topological insulator and robust one-way sound transport
He, C. et al · 2016
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Probing topological protection using a designer surface plasmon structure
Gao, F. et al · 2016
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Photonics and optoelectronics of 2d semiconductor transition metal dichalcogenides
Mak, K. F. & Shan, J · 2016
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Non-abelian braiding of light
Iadecola, T., Schuster, T. & Chamon, C · 2016
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Quantized electric multipole insulators
Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L · 2017
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Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators
Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L · 2017
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Reflection-symmetric second-order topological insulators and superconductors
Langbehn, J., Peng, Y., Trifunovic, L., von Oppen, F. & Brouwer, P. W · 2017
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(d-2)-dimensional edge states of rotation symmetry protected topological states
Song, Z., Fang, Z. & Fang, C · 2017
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Higher-order topological insulators and superconductors
T. Neupert, F. A. M · 2017
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Two-dimensional topological photonics
Khanikaev, A. B. & Shvets, G · 2017
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Novel topological phase with a zero berry curvature
Liu, F. & Wakabayashi, K · 2017
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Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice
Mukherjee, S. et al · 2017
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2d transition metal dichalcogenides
Manzeli, S., Ovchinnikov, D., Pasquier, D., Yazyev, O. V. & Kis, A · 2017
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Scalable designs for quasiparticle-poisoning-protected topological quantum computation with majorana zero modes
Karzig, T. et al · 2017
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Weyl and dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J. & Vishwanath, A · 2018
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Higher-order topological insulators
Schindler, F. et al · 2018
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Second-order topological insulators and superconductors with an order-two crystalline symmetry
Geier, M., Trifunovic, L., Hoskam, M. & Brouwer, P. W · 2018
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Majorana kramers pairs in higher-order topological insulators
Hsu, C.-H., Stano, P., Klinovaja, J. & Loss, D · 2018
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Topological protection of photonic mid-gap defect modes
Noh, J. et al · 2018
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Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices
Ezawa, M · 2018
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Minimal models for wannier-type higher-order topological insulators and phosphorene
Ezawa, M · 2018
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Topological switch between second-order topological insulators and topological crystalline insulators
Ezawa, M · 2018
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Higher-order topological insulators and superconductors protected by inversion symmetry
Khalaf, E · 2018
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Majorana kramers pairs in higher-order topological insulators
Hsu, C.-H., Stano, P., Klinovaja, J. & Loss, D · 2018
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Connecting higher-order topological insulators to lower-dimensional topological insulators
Matsugatani, A. & Watanabe, H · 2018
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Higher-order topology in bismuth
Schindler, F. et al · 2018
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Higher-order topological insulators protected by inversion and rotoinversion symmetries
Van Miert, G. & Ortix, C · 2018
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Observation of a phononic quadrupole topological insulator
Serra-Garcia, M. et al · 2018
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A quantized microwave quadrupole insulator with topologically protected corner states
Peterson, C. W., Benalcazar, W. A., Hughes, T. L. & Bahl, G · 2018
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Topolectrical-circuit realization of topological corner modes
Imhof, S. et al · 2018
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Second-order photonic topological insulator with corner states
Xie, B.-Y. et al · 2018
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Photonics meets topology
Xie, B.-Y. et al · 2018
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Topological sound
Zhang, X., Xiao, M., Cheng, Y., Lu, M.-H. & Christensen, J · 2018
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Lattice models with exactly solvable topological hinge and corner states
Kunst, F. K., van Miert, G. & Bergholtz, E. J · 2018
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High-temperature majorana corner states
Wang, Q., Liu, C.-C., Lu, Y.-M. & Zhang, F · 2018
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Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
Liu, T., He, J. J., Nori, F. et al · 2018
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Tunable majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
Zhu, X · 2018
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Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials
Yang, Y. et al · 2018
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Interacting topological insulators: a review
Rachel, S · 2018
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Higher-order topological electric circuits and topological corner resonance on the breathing kagome and pyrochlore lattices
Ezawa, M · 2018
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Inversion-symmetry protected chiral hinge states in stacks of doped quantum hall layers
Kooi, S. H., Van Miert, G. & Ortix, C · 2018
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Magnetic second-order topological insulators and semimetals
Ezawa, M · 2018
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Surfaces of axion insulators
Varnava, N. & Vanderbilt, D · 2018
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Non-hermitian physics and pt symmetry
El-Ganainy, R. et al · 2018
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Non-hermitian chern bands
Yao, S., Song, F. & Wang, Z · 2018
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Topological protection of biphoton states
Blanco-Redondo, A., Bell, B., Oren, D., Eggleton, B. J. & Segev, M · 2018
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A topological quantum optics interface
Barik, S. et al · 2018
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Higher-order symmetry-protected topological states for interacting bosons and fermions
You, Y., Devakul, T., Burnell, F. J. & Neupert, T · 2018
Cited alongside, same era.
Perovskites for light emission
Quan, L. N., García de Arquer, F. P., Sabatini, R. P. & Sargent, E. H · 2018
Cited alongside, same era.
Higher-order topological insulator in twisted bilayer graphene
Park, M. J., Kim, Y., Cho, G. Y. & Lee, S · 2019
Cited alongside, same era.
Higher-order topological odd-parity superconductors
Yan, Z · 2019
Cited alongside, same era.
Higher-order topological mott insulators
Kudo, K., Yoshida, T. & Hatsugai, Y · 2019
Cited alongside, same era.
Splitting the hinge mode of higher-order topological insulators
Queiroz, R. & Stern, A · 2019
Cited alongside, same era.
Acoustic realization of quadrupole topological insulators
Qi, Y. et al · 2020
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Observation of an acoustic octupole topological insulator
Xue, H. et al · 2020
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Demonstration of a quantized acoustic octupole topological insulator
Ni, X., Li, M., Weiner, M., Alù, A. & Khanikaev, A. B · 2020
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Octupole corner state in a three-dimensional topological circuit
Liu, S. et al · 2020
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Demonstration of a third-order hierarchy of topological states in a three-dimensional acoustic metamaterial
Weiner, M., Ni, X., Li, M., Alù, A. & Khanikaev, A. B · 2020
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Multidimensional sound propagation in 3d high-order topological sonic insulator
Meng, F. et al · 2020
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Two-dimensional second-order topological insulator in graphdiyne
Sheng, X.-L. et al · 2019
Cited alongside, same era.
Multipolar topological field theories: Bridging higher order topological insulators and fractons
You, Y., Burnell, F. & Hughes, T. L · 2019
Cited alongside, same era.
Higher-order bulk-boundary correspondence for topological crystalline phases
Trifunovic, L. & Brouwer, P. W · 2019
Cited alongside, same era.
Efficient topological materials discovery using symmetry indicators
Tang, F., Po, H. C., Vishwanath, A. & Wan, X · 2019
Cited alongside, same era.
Topoelectrical circuit octupole insulator with topologically protected corner states
Bao, J. et al · 2019
Cited alongside, same era.
Realization of an acoustic third-order topological insulator
Xue, H. et al · 2019
Cited alongside, same era.
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Three-dimensional higher-order topological acoustic system with multidimensional topological states
Zheng, S. et al · 2020
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Twisted quadrupole topological photonic crystals
Zhou, X. et al · 2020
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Anomalous quadrupole topological insulators in two-dimensional nonsymmorphic sonic crystals
Lin, Z.-K., Wang, H.-X., Xiong, Z., Lu, M.-H. & Jiang, J.-H · 2020
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Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals
Zhang, X. et al · 2020
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Plasmon-polaritonic quadrupole topological insulators
Chen, Y., Lin, Z.-K., Chen, H. & Jiang, J.-H · 2020
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Topological edge and corner states in a two-dimensional photonic su-schrieffer-heeger lattice
Kim, M. & Rho, J · 2020
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Quadrupole topological photonic crystals
He, L., Addison, Z., Mele, E. J. & Zhen, B · 2020
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Higher-order topological states in surface-wave photonic crystals
Zhang, L. et al · 2020
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Higher-order topological states in photonic kagome crystals with long-range interactions
Li, M. et al · 2020
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Gapped topological kink states and topological corner states in honeycomb lattice
Yang, Y. et al · 2020
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A higher-order topological insulator with wide bandgaps in lamb-wave systems
Wang, Z., Wei, Q., Xu, H.-Y. & Wu, D.-J · 2020
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Observation of symmetry-protected zero modes in topolectrical circuits
Yang, H., Li, Z.-X., Liu, Y., Cao, Y. & Yan, P · 2020
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Higher-order topological phases in a spring-mass model on a breathing kagome lattice
Wakao, H., Yoshida, T., Araki, H., Mizoguchi, T. & Hatsugai, Y · 2020
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Wang, Y. et al · 2020
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Corner states in second-order mechanical topological insulator
Chen, C.-W., Chaunsali, R., Christensen, J., Theocharis, G. & Yang, J · 2020
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On-chip higher-order topological micromechanical metamaterials
Wu, Y., Yan, M., Wang, H.-X., Li, F. & Jiang, J.-H · 2020
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Coupling between exciton-polariton corner modes through edge states
Banerjee, R., Mandal, S. & Liew, T · 2020
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Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
Xiong, Z. et al · 2020
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Recent advances in 2d, 3d and higher-order topological photonics
Kim, M., Jacob, Z. & Rho, J · 2020
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Topological phononics: From fundamental models to real materials
Liu, Y., Chen, X. & Xu, Y · 2020
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Engineering corner states from two-dimensional topological insulators
Ren, Y., Qiao, Z. & Niu, Q · 2020
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A fractional corner anomaly reveals higher-order topology
Peterson, C. W., Li, T., Benalcazar, W. A., Hughes, T. L. & Bahl, G · 2020
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Braiding majorana corner modes in a second-order topological superconductor
Pahomi, T. E., Sigrist, M. & Soluyanov, A. A · 2020
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Inversion-protected higher-order topological superconductivity in monolayer wte 2 {\mathrm{wte}}_{2}
Hsu, Y.-T., Cole, W. S., Zhang, R.-X. & Sau, J. D · 2020
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Spin-orbit-parity-coupled superconductivity in topological monolayer wte 2 {\mathrm{wte}}_{2}
Xie, Y.-M., Zhou, B. T. & Law, K. T · 2020
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Vortex and surface phase transitions in superconducting higher-order topological insulators
Ghorashi, S. A. A., Hughes, T. L. & Rossi, E · 2020
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Higher-order weyl semimetals
Wang, H.-X., Lin, Z.-K., Jiang, B., Guo, G.-Y. & Jiang, J.-H · 2020
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Higher-order weyl semimetals
Ghorashi, S. A. A., Li, T. & Hughes, T. L · 2020
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Observation of a phononic higher-order weyl semimetal
Luo, L. et al · 2020
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Higher-order quantum spin hall effect in a photonic crystal
Xie, B. et al · 2020
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Higher-order topological spin hall effect of sound
Lin, Z.-K., Wu, S.-Q., Wang, H.-X. & Jiang, J.-H · 2020
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Pseudospin induced topological corner state at intersecting sonic lattices
Zhang, Z. et al · 2020
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Fractional chiral hinge insulator
Hackenbroich, A., Hudomal, A., Schuch, N., Bernevig, B. A. & Regnault, N · 2020
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Evidence of higher order topology in multilayer wte2 from josephson coupling through anisotropic hinge states
Kim, K. C. F., Ali, M. N., Law, K. T. & Lee, G.-H · 2020
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Reducing electronic transport dimension to topological hinge states by increasing geometry size of dirac semimetal josephson junctions
Li, C.-Z. et al · 2020
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Unhinging the surfaces of higher-order topological insulators and superconductors
Tiwari, A., Li, M.-H., Bernevig, B. A., Neupert, T. & Parameswaran, S. A · 2020
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Higher-order topological insulators in synthetic dimensions
Dutt, A., Minkov, M., Williamson, I. A. & Fan, S · 2020
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Higher-order topological insulators, topological pumps and the quantum hall effect in high dimensions
Petrides, I. & Zilberberg, O · 2020
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Higher-order topological insulators in amorphous solids
Agarwala, A., Juričić, V. & Roy, B · 2020
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Higher-order topological insulators in quasicrystals
Chen, R., Chen, C.-Z., Gao, J.-H., Zhou, B. & Xu, D.-H · 2020
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Kane-mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
Spurrier, S. & Cooper, N. R · 2020
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Higher-order topological insulator in a dodecagonal quasicrystal
Hua, C.-B., Chen, R., Zhou, B. & Xu, D.-H · 2020
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Bound states in the continuum of higher-order topological insulators
Benalcazar, W. A. & Cerjan, A · 2020
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Experimental discovery of bulk-disclination correspondence
Liu, Y. et al · 2020
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Peterson, C. W., Li, T., Jiang, W., Hughes, T. L. & Bahl, G · 2020
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Ashida, Y., Gong, Z. & Ueda, M · 2020
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Wannier-type photonic higher-order topological corner states induced solely by gain and loss
Wu, Y.-J., Liu, C.-C. & Hou, J · 2020
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Non-hermitian route to higher-order topology in an acoustic crystal
Gao, H. et al · 2020
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Dynamical singularities of floquet higher-order topological insulators
Hu, H., Huang, B., Zhao, E. & Liu, W. V · 2020
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Floquet higher-order topological insulators with anomalous dynamical polarization
Huang, B. & Liu, W. V · 2020
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Higher order topological insulator via periodic driving
Ghosh, A. K., Paul, G. C. & Saha, A · 2020
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Second-order topological insulator in a coinless discrete-time quantum walk
Meng, Y., Chen, G. & Jia, S · 2020
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Entanglement signatures of multipolar higher order topological phases
Dubinkin, O. & Hughes, T. L · 2020
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Symmetry-protected zero modes in metamaterials based on topological spin texture
Li, Z.-X., Cao, Y., Wang, X. R. & Yan, P · 2020
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Higher-order photonic topological insulator metasurfaces
Dia’aaldin, J. B. & Sievenpiper, D. F · 2020
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Nonlinear topological photonics
Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y · 2020
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Interaction-induced lattices for bound states: Designing flat bands, quantized pumps, and higher-order topological insulators for doublons
Salerno, G., Palumbo, G., Goldman, N. & Di Liberto, M · 2020
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Nonlinear higher-order polariton topological insulator
Zhang, Y., Kartashov, Y., Torner, L., Li, Y. & Ferrando, A · 2020
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Cavity quantum electrodynamics with second-order topological corner state
Xie, X. et al · 2020
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Measurement-only quantum computation with floquet majorana corner modes
Bomantara, R. W. & Gong, J · 2020
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Braiding photonic topological zero modes
Noh, J. et al · 2020
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Higher-order topological semimetal in phononic crystals
Wei, Q. et al · 2020
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Zero-energy corner states in a non-hermitian quadrupole insulator
Yu, Y., Jung, M. & Shvets, G · 2021
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