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Weyl points: Wanted for 86 years

Massachusetts Institute of Technology, Institute for Soldier Nanotechnologies

Weyl points, the 3D analogues of the structures that make graphene exceptional, were theoretically predicted in 1929. Today, an international team of Physicists from MIT and Zhejiang University, found them in photonic crystals, opening a new dimension in photonics.

In 1928 the English physicist Paul Dirac discovered a crucial equation in particle physics and quantum mechanics, now known as Dirac equation, which describes relativistic wave-particles. Very fast electrons were solutions to the Dirac equation. Moreover, the equation predicted the existence of anti-electrons, or positrons: particles with the same mass as electrons but having opposite charge. True to Dirac's prediction, positrons were discovered four years later, in 1932, by the American physicist Carl Anderson. In 1929 Hermann Weyl, a German-born mathematician, found another solution to the Dirac equation, this time massless [1]. A year later, the Austrian-born theoretical physicist Wolfgang Pauli postulated the existence of the neutrino, which was then thought to be massless, and it was assumed to be the sought-after solution to the Dirac equation found by Weyl. Neutrinos had not been detected yet in nature, but the case seemed to be closed. It would be decades before American physicists Frederick Reines and Clyde Cowan finally discovered neutrinos in 1957, and numerous experiments shortly thereafter indicated that neutrinos could have mass. In 1998, the Super-Kamiokande (a neutrino observatory located in Japan) Collaboration announced what had now been speculated for years: neutrinos have non-zero mass. This discovery opened a new question: what then was the zero-mass solution found by Weyl?

Dr. Ling Lu (MIT), Dr. Zhiyu Wang (Zhejiang University, China), Dr. Dexin Ye (Zhejiang University), Prof. Lixin Ran (Zhejiang University), Prof. Liang Fu (MIT), Prof. John D. Joannopoulos (MIT), and Prof. Marin Soljači? (MIT) found the answer.

Ling Lu, first author of the paper published in Science, is very enthusiastic: "Weyl points do actually exist in nature! We built a double-gyroid photonic crystal with broken parity symmetry. The light that passes through the crystal shows the signature of Weyl points in reciprocal space: two linear dispersion bands touching at isolated points." Weyl points, the solutions to the massless Dirac equation, were not found in particle experiments. The research team had to build a tailored material to observe them. The double-gyroid photonic crystal is itself a work of art. Gyroids indeed can be found in nature, in systems as different as butterfly wings and ketchup [2,3]. However, the research group wanted a double-gyroid with a very specific broken symmetry, first proposed in a theoretical work by the same group[4]. In order to fabricate this structure, with parts that are interlocking and with ad hoc defects (such as symmetry-breaking air holes), Lu and collaborators had to drill, machine, and stack slabs of ceramic-filled plastics (Figure 1).

Once the sample was ready, it was time to observe if it behaved as expected, by shining light through it and analyzing the outgoing signal. Physicists analyze these experiments in what is called reciprocal space, or momentum space. The right panel in Figure 2 shows what Weyl points are supposed to look like in reciprocal space: degenerate points, points where two linear dispersion bands meet. The left panel shows an example of the measured data, the solid proof that Weyl points do indeed exist in nature.

"The discovery of Weyl points is not only the smoking gun to a scientific mystery," comments MIT Professor Marin Soljači?, "it paves the way to absolutely new photonic phenomena and applications. Think of the graphene revolution: graphene is a 2D structure, and its electronic properties are, to a substantial extent, a consequence of the existence of linear degeneracy points (known as Dirac points) in its momentum space. Materials containing Weyl points do the same in 3D. They literally add one degree of freedom, one dimension." The discovery of graphene and its unique electronic properties was lauded with the 2010 Nobel Prize in physics, yet graphene's Dirac points are not stable to perturbations. On the other hand, the structures introduced by Lu et al. are very stable to perturbations*, offering a new tool to control how light is confined, how it bounces, and how it radiates. This discovery opens a new intriguing field in basic physics. The potential applications are equally promising. Examples include the possibility to build angularly selective 3D materials and more powerful single-frequency lasers.


* The stability of 3D Weyl points is due to the fact that they are topological monopoles. Monopoles can occur in two varieties, e.g. positive and negative. By analogy, electric monopoles are positive and negative charges. Electric charge is conserved, therefore electric monopoles can only be created or annihilated in pairs (positive and negative neutralize). The same is true for topological monopoles: they can only appear or disappear in pairs, making them more robust to perturbations. On the contrary, graphene's Dirac points are not topological monopoles: they are neutral, meaning that they do not need a companion to appear or disappear.

RESEARCH PAPER: "Experimental observation of Weyl points", Ling Lu, Zhiyu Wang, Dexin Ye, Lixin Ran, Liang Fu, John D. Joannopoulos, and Marin Soljači?, Science URL:


Prof. Marin Soljači?


  1. H. Weyl, "Elektron und gravitation," Z. Phys. 56, 330- 352 (1929)
  2. V. Saranathan, et al. "Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales."Proc. Natl Acad. Sci. USA 107, 11676-11681(2010).
  3. W. Longley, & , T. J. McIntosh "A bicontinuous tetrahedral structure in a liquid-crystalline lipid" Nature 303, 612-614 (1983)
  4. L. Lu, L. Fu, J. D. Joannopoulos and M. Soljači? "Weyl points and line nodes in gyroid photonic crystals" Nature Photonics, Vol. 7, No. 4, P. 294-299 (2013)
  5. J. Fleischer "Achieving robust Weyl points", news &views Nature Photonics Vol 7 No 3 (2013) Written by Dr. Paola Rebusco (

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