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Topological semimetals with helicoid surface states

Nature Physics volume 12, pages 936941 (2016) | Download Citation

Abstract

We show that the surface dispersions of topological semimetals map to helicoidal structures, where the bulk nodal points project to the branch points of the helicoids whose equal-energy contours are Fermi arcs. This mapping is demonstrated in the recently discovered Weyl semimetals and leads us to predict new types of topological semimetals, whose surface states are represented by double- and quad-helicoid surfaces. Each helicoid or multi-helicoid is shown to be the non-compact Riemann surface representing a multi-valued holomorphic function (generating function). The intersection of multiple helicoids, or the branch cut of the generating function, appears on high-symmetry lines in the surface Brillouin zone, where surface states are guaranteed to be doubly degenerate by a glide reflection symmetry. We predict the heterostructure superlattice [(SrIrO3)2(CaIrO3)2] to be a topological semimetal with double-helicoid surface states.

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Acknowledgements

We thank T. H. Hsieh for discussions. C.F. thanks Y. Chen for helpful discussions on the tight-binding model. C.F. thanks J.L. for fruitful discussions on potential material systems. C.F. and L.F. were supported by S3TEC Solid State Solar Thermal Energy Conversion Center, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award no. DE-SC0001299/DE-FG02-09ER46577. C.F. was also supported by the National Thousand-Young-Talents Program of China. L.L. was supported in part by USARO through the ISN under Contract no. W911NF-13-D-0001, in part by the MRSEC Program of the NSF under Award no. DMR-1419807, and in part by the MIT S3TEC EFRC of DOE under Grant no. DE-SC0001299. J.L. was supported by the STC Center for Integrated Quantum Materials, NSF Grant no. DMR-1231319.

Author information

Author notes

    • Chen Fang
    •  & Ling Lu

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Chen Fang
    • , Ling Lu
    • , Junwei Liu
    •  & Liang Fu
  2. Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

    • Chen Fang
    •  & Ling Lu

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Contributions

C.F. and L.L. conceived the mapping between surface state dispersions and helicoids; L.F. planned the project; C.F. and L.F. performed the band topology analysis; J.L. performed the first-principles calculation and all authors contributed to the preparation of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Chen Fang or Liang Fu.

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DOI

https://doi.org/10.1038/nphys3782

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