Kramers-Weyl Fermions in Chiral Crystals

Post Date:2018-12-24

The discovery of Weyl semimetal TaAs was highlighted as one of the Top Ten Breakthroughs in year 2015 by Physics World. The prediction of the nontrivial band topology in TaAs was made by Dr. Hsin Lin’s theory group using first-principles electronic structures calculations, followed by its experimental verification done by their collaborators in Princeton University. Since Hermann Weyl proposed Weyl equations in 1929, the Weyl fermion has not been observed in high energy/particle physics. The electronic band structures of crystalline TaAs can host quasiparticles obeying Weyl equations and are topologically nontrivial. The study of Weyl fermions has become a hot topic at the present forefront research.

Weyl fermions carry topological chiral charges and always appear in pairs of opposite chirality. Two Weyl fermions with opposite chirality are connected by Fermi arcs on the surface of crystals. The pairwise creation and annihilation of Weyl fermions usually involve a band inversion. On the other hand, crystal structures can also exhibit chirality. The mirror image of a chiral crystal cannot be superimposed on itself. The universal link betwenn topological chiral charges and structural chirality is recently revealed by Dr. Hsin Lin’s group and collaborators in Nature Materials 17, 978, (2018). The article is also highlighted in Nature Materials news & views. (doi: 10.1038/s41563-018-0210-6).

Combining the first-principles electronic band structures calculations and topological band theory, they found the nonmagnetic chiral crystals generally host Weyl fermions on the time-reversal-invariant points in the reciprocal lattice when the spin-orbit coupling is present. Since Nonmagnetic chiral crystals preserve the time-reversal symmetry, according to Kramers theorem, the spin up and down electronic states have to be degenerate on the time-reversal-invariant points. The quasiparticles around the degeneracy obey Weyl equations, and these new type of fermions are termed Kramers-Weyl fermions. The traditional Weyls fermions are related to band inversions, and the strength of the band inversion is proportional to the length of the surface Fermi arcs. On the contrary, Kramers-Weyl fermions do not require the band inversion and are connected by the longest possible Fermi arcs connecting the Brillouin zone center and corners. As shown in Figure 1, Fermi arcs are predicted between the Brillouin zone center and corners on the [001] surface of chiral crystal CoSi.

Dr. Hsin Lin’s theory group has established effective collaborations with several of the world’s leading experimental groups to enable rapid synthesis, characterization and physical realization of the most promising predicted candidate materials. This year (2018), they have two publications in Nature, one in collaboration with a team in Nanyang Technological University in Singapore, see Nature 562, 91 (2018), and the other with Princeton University, see Nature 556, 355 (2018). Physics involving the spin-orbit coupling in 2D materials, topological materials, magnetic materials, superconducting materials, and metals would remain important at the forefront research. The first-principles electronic structure calculations have been proven to be a powerful tool in this field. Dr. Lin’s theoretical study on thousands of chiral crystals would advance the realization of Kramers-Weyl fermions in experiment very soon.

Figure 1:Theoretical prediction of large Fermi arcs connecting the Brillouin zone center and corners on the [001] surface of chiral crystal CoSi.


  1. Nature Materials, published on October 1, 2018 Topological quantum properties of chiral crystals https://rdcu.be/9vei

  2. Nature volume 562, 91 (12 September 2018) Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet https://rdcu.be/9ve5

  3. Nature Communications volume 9, Article number: 4153 (2018) Quasiparticle interference and nonsymmorphic effect on a floating band surface state of ZrSiSe https://rdcu.be/9vdr


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