Weyl points and line nodes are three-dimensional linear point and line degeneracies between two bands. In contrast to two-dimensional Dirac points, which are their lower-dimensional analogues, Weyl points are stable in momentum space, and the associated surface states are predicted to be topologically non-trivial. However, Weyl points are yet to be discovered in nature. Here, we report photonic crystals based on double-gyroid structures, exhibiting frequency-isolated Weyl points with complete phase diagrams by breaking the parity and time-reversal symmetries. Gapless surface dispersions associated with non-zero Chern numbers are demonstrated. Line nodes are also found in similar geometries, the associated surface states forming flat dispersion bands. Our results are based on realistic ab initio calculations with true predictive power and should be readily realizable experimentally from microwave to optical frequencies.
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The authors thank F. Wang, M. Maldovan, Y. Ran, Z. Wang, S. G. Johnson, A. Vishwanath and D-H. Lee for helpful discussions. This work was supported in part by the US Army Research Office through the Institute for Soldier Nanotechnologies (contract no.W911NF-07-D-0004). L.L. was supported in part by the Materials Research Science and Engineering Center of the National Science Foundation (award no. DMR-0819762). M.S. and L.L. were supported in part by the Massachusetts Institute of Technology S3TEC Energy Frontier Research Center of the US Department of Energy (grant no. DE-SC0001299). L.F. was supported by start-up funds from MIT.
The authors declare no competing financial interests.
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Lu, L., Fu, L., Joannopoulos, J. et al. Weyl points and line nodes in gyroid photonic crystals. Nature Photon 7, 294–299 (2013). https://doi.org/10.1038/nphoton.2013.42
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