Research Article

Wallpaper fermions and the nonsymmorphic Dirac insulator

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Science  20 Jul 2018:
Vol. 361, Issue 6399, pp. 246-251
DOI: 10.1126/science.aan2802

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Exotic topology on the surface

Analyzing the spatial symmetries of three-dimensional (3D) crystal structures has led to the discovery of exotic types of quasiparticles and topologically nontrivial materials. Wieder et al. focus on the symmetry groups of 2D surfaces of 3D materials—the so-called wallpaper groups—and find that some of them allow for an additional topological class. This class hosts a single fourfold-degenerate Dirac fermion on the surface of the material and, on the basis of the authors' calculations, is expected to occur in the compound Sr2Pb3.

Science, this issue p. 246


Materials whose gapless surface states are protected by crystal symmetries include mirror topological crystalline insulators and nonsymmorphic hourglass insulators. There exists only a very limited set of possible surface crystal symmetries, captured by the 17 “wallpaper groups.” Here we show that a consideration of symmetry-allowed band degeneracies in the wallpaper groups can be used to understand previously described topological crystalline insulators and to predict phenomenologically distinct examples. In particular, the two wallpaper groups with multiple glide lines, pgg and p4g, allow for a topological insulating phase whose surface spectrum consists of only a single, fourfold-degenerate, true Dirac fermion, representing an exception to a symmetry-enhanced fermion-doubling theorem. We theoretically predict the presence of this phase in Sr2Pb3 in space group 127 (P4/mbm).

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