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“Topology in materials science”

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Topological insulators, Weyl and Dirac Semimetals are a new quantum state of matter, which have attracted interest of condensed matter science. Tunable families of compounds such as Heusler compounds, binary phosphides and chalcogenides allows for a design of these new properties and their systematic study. Many known compounds were reclassified through the lens of topology. Heusler compounds are a remarkable class of materials with more than 1,000 members and a wide range of extraordinary multifunctionalities [1] including tunable topological insulators (TI) [2,3] and Weyl semimetals [4,5]. Many of these ternary zero-gap semiconductors in Heusler compounds (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi) to magnetism (for example GdPtBi) and heavy fermion behavior (for example YbPtBi). These properties can open new research directions in realizing the quantized anomalous Hall Effect and topological superconductors. C1b Heusler compounds have been grown as single crystals and as thin films. The band inversion is proven by ARPES [6] and a large anomalous Hall can be explained within a Weyl-Berry curvature scenario. Binary phoshides are the ideal material class for a systematic study of Dirac and Weyl physics. Weyl points, a new class of topological phases was also predicted in NbP, NbAs. TaP, MoP and WP2 . [7-11]. New Fermions beyond Weyl and Dirac have been predicted by Bernevig’s team and can be classified by space groups and Wyckoff positions [12]. The new fermion MoP and the Weyl semimetal WP2 show extremely low resistance despite a high mobility. More emerging quantum properties and potential applications will be discussed.

  1. Tanja Graf, Stuart S. P. Parkin, and Claudia Felser, Progress in Solid State Chemistry 39 (2011) 1
  2. S. Chadov, X. Qi, J. Kübler, G. H. Fecher, C. Felser, S.-C. Zhang, Nature Mat. 9 (2010) 541
  3. H. Lin, et al., Nature Mat. 9 (2010) 546
  4. M. Hirschberger et al., Nature Mat. 15, (2016) 1161
  5. C. Shekhar, et al., preprint: arXiv: 1604.01641
  6. Z. K. Liu, et al., Nature Communication 7 (2016) 12924
  7. C. Shekhar, et al., Nature Physics 11 (2015) 645
  8. Z. K. Liu, et al., Nature Mat. 15 (2016) 27
  9. L. Yang, et al., Nature Physics 11 (2015) 728
  10. C. Shekhar, et al. preprint arXiv:1703.03736
  11. N. Kumar, et al. preprint arXiv:1703.04527
  12. B. Bradlyn, et al., Science 353 (2016) aaf5037

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