Weyl points and line nodes in gyroid photonic crystals

Abstract

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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Figure 1: Real-space unit cell and reciprocal-space Brillouin zone of the gyroid photonic crystals.
Figure 2: Gapless photonic band structures of the DG photonic crystals.
Figure 3: Flat surface dispersions of two pseudo-gapped photonic crystals.
Figure 4: Phase diagram of Weyl points when the magnetic field is applied along Γ-N.
Figure 5: Topological surface states of a Weyl-point photonic crystal.

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Acknowledgements

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.

Author information

L.L. proposed the gyroid photonic crystal system for realizing Weyl points and performed the simulations. L.F. developed a low-energy k.p model for the proposed system. All authors contributed to the design of the study, discussion of the results and writing of the manuscript.

Correspondence to Ling Lu.

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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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