Welcome to the Department of Topological Quantum Chemistry

The main research areas of the Topological Quantum Chemistry group are related to the design, synthesis, and investigation of new quantum materials with topological properties (1,2) and Heusler compounds (3, 4, 5). We use design rules that enable the finding of materials with properties on demand. Based on the structural and electronic structure relation between semiconductors such as GaAs or HgTe it is possible to design new topological insulators within the class of Heusler compounds XYZ with C1_b structure type, semiconductors with additional properties such as superconductivity or magnetism (6). This allows eventually the realization of Majorana fermions and quantum anomalous Hall effect (6). Further examples of our work in topology include: Bernevig and Felser: topological quantum chemistry (1, 2) and new Fermions (7) and the subgroup of chiral Fermions (8, 9); discovery of Weyl fermions (10), in nonmagnetic NbP and TaAs (11, 12, 13, 14) and WP₂ (15, 16, 17). The axial gravitational anomaly was identified with co-workers around Gooth in NbP (18). We predicted the magnetic Weyl semimetals in Mn₃Ge, Mn₃Sn Co₂MnGa and Co₃Sn₂S₃ (19, 20, 21, 22) and realized by us as high quality single crystals and proven in collaboration with groups from Princeton, Weizmann and Oxford in Mn₃Ge (23), Co₃Sn₂S₂ (22, 24, 25) and Co₂MnGa (26, 27).
We have an elegant set of design rules for Heusler compounds (3 - 5) that allow devolopment for many applications including quantum and energy applications. Heusler compounds with X₂YZ with L2₁ and XYZ with C1_b structure type – show the same broad variety of properties comparable to the perovskites, including topological insulators (6), Kondo behavior, non-centrosymmetric superconductivity and conventional, tunable magnetic properties (28), non-collinear magnetism (29, 23), semiconductivity, magnetoresistance effects,  Li-ion-conductivity and other physical properties. Examples are the semiconducting Half Heusler compounds for thermoelectric applications (4) and the ferrimagnetic  Mn₂YZ Heusler compounds for Skyrmions (30) and spintronic applications (31, 5, 23). These concepts can be transferred to other families of materials such as perovskites and skutterudites.