In the last decade, since the groundbreaking discovery of spin-orbit induced topological insulators, tremendous progress has been made in our understanding of topological states of matter [1-3]. Although topologically nontrivial properties are normally associated with insulating phases, certain semimetals and nodal superconductors can also be topological. That is, the bulk band structure of these materials has a nontrivial topology which protects an even number of gap closing points. The low-energy excitations near these gap closing points can be described as emergent relativistic quasiparticles, which often have Dirac, Weyl or Majorana character.
One aim of this research project is to systematically search for new gapless topological materials. This requires the classification of topological distinct Bloch and Bogoliubov-de Gennes band structures for the 230 nonmagnetic and 1651 magnetic space groups in three dimensions [4-8]. We will attack this classification problem using Clifford analysis and K-theory and subsequently derive the corresponding topological invariants. Implementing the calculation of these invariants within DFT ab-initio codes will allow us to scan large databases (e.g., ICSD from FIZ Karlsruhe  or the Materials Project Database ) for new topological systems.
Another aim of this research project is to study and characterize the exotic phenomena associated with the nontrivial topologies of Weyl, Dirac, and Majorana nodes. One example is the appearance of unusual boundary modes that can exist only at the surface of topological semimetals and topological superconductors.
Other remarkable phenomena that we plan to investigate include the chiral magnetic effect, the parity anomaly, the chiral anomaly, and the gravitational anomaly. We will study how these quantum anomalies are connected to unusual transport properties of the topological semimetals and topological superconductors. While this project mainly aims at the characterization of the fundamental properties of topological quantum matter, the insights gained within this research project may have important implications for potential applications in spintronics and for low-power and high-speed electronics.
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 C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Rev. Mod. Phys. 88, 035005 (2016).
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 Y. X. Zhao, Andreas P. Schnyder, and Z. D. Wang, Phys. Rev. Lett. 116, 156402 (2016).
 Y. X. Zhao and Andreas P. Schnyder, arXiv:1606.03698.
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Andreas P. Schnyder (MPI), email@example.com
Marcel Franz (UBC), firstname.lastname@example.org
Dirk Manske (MPI), email@example.com