Topological and geometrical properties of electronic wavefunctions can lead to a variety of interesting phenomena in real materials. Examples include the integer quantum Hall effect in the absence of an external magnetic field, the quantum spin Hall effect, protected metallic states, among others. Moreover, for superconducting systems the band geometry gives rise to non-Abelian quasiparticles, which are the main ingredient for realizing schemes of topologically protected quantum computing.
We are concerned with the discovery of novel band topologies in matter. Our approach includes theoretical prediction of novel states as well as the identification of material canditates that actually host them. Research directions include topological semi-metals as well as topological insulators and superconductors. The picture shows a special kind of Fermion appearing only inside of materials, the Weyl-Fermion. Today we know of two kinds of Weyl Fermions, the type-I and type-II, of which the later kind was theoretically discovered in our group: A New Type of Weyl Semimetals
Our material search is powered by large scale ab initio simulations running on state-of the art computational clusters and supercomputers. Downfolding the band structure onto first-principles derived tight-binding models allows us to realistically simulate real devices and optimise conditions for realizing topological phenomena in them.
In addition to using established state-of-the-art simulation codes, we are striving to create new methods for identifying topological states. We developed the Z2Pack software, which is an open-source library for computing topological invariants. It allows us to compute these invariants for any model or system, be it from first-principles calculations, tight-binding or k.p models.