The topological phases of matter are characterized using the Berry phase, a geometrical phase associated with the energy-momentum band structure. The quantization of the Berry phase and the associated wavefunction polarization manifest as remarkably robust physical observables, such as quantized Hall conductivity and disorder-insensitive photonic transport1,2,3,4,5. Recently, a novel class of topological phases, called higher-order topological phases, were proposed by generalizing the fundamental relationship between the Berry phase and quantized polarization, from dipole to multipole moments6,7,8. Here, we demonstrate photonic realization of the quantized quadrupole topological phase, using silicon photonics. In our two-dimensional second-order topological phase, we show that the quantization of the bulk quadrupole moment manifests as topologically robust zero-dimensional corner states. We contrast these topological states against topologically trivial corner states in a system without bulk quadrupole moment, where we observe no robustness. Our photonic platform could enable the development of robust on-chip classical and quantum optical devices with higher-order topological protection.
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The data that support the findings of this study are available from the corresponding author on reasonable request.
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This research was supported by AFOSR-MURI FA9550-14-1-0267, the Sloan Foundation and the Physics Frontier Center at the Joint Quantum Institute. A.P. and M.A.G. have been supported by the Russian Foundation for Basic Research grant no. 18-29-20037 and the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS. A.P. also acknowledges partial support by the Australian Research Council. The authors thank H. Dehghani, Y. Kivshar and D. Leykam for discussions and E. Yamaguchi and J. Vannucci for experimental help.
The authors declare no competing interests.
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Supplementary derivations, discussion and experimental data. Supplementary Figs. 1–10 and Supplementary references 1–6.
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Nature Photonics (2019)
Physical Review B (2019)