The heart of this SFB is to study the interplay of spin-orbit coupling and electron-electron interactions, which could lead to new topological phases of matter. One of the still undiscovered topological phases is topological superconductivity. It is therefore an open challenge, which is also the goal of this proposal, to predict clear signatures of topological and unconventional superconductivity in spectral functions, dI/dV characteristics, as well as spin and charge transport. Here, we will focus on two classes of systems: (1) Hybrid structures built from 3D topological insulators (TIs) and superconductors and (2) artificially engineered two-dimensional structures which can be tuned in the topological superconductor phase. In the first class of materials, the proximity effect between the surface state of a topological insulator and a singlet superconductor leads to a mixed superconducting condensate with singlet and triplet pairing. The relevant question here is how to tune the ratio of singlet and triplet pairings to design a setup, so only the unconventional triplet component is relevant in both dc and ac Josephson junctions. Further, we will study possibilities to engineer a magnetic field, so that only the coupling to the triplet component of the superconducting condensate is possible, and one induces the superconducting transverse response (Hall effect), just due to the unconventional part of the superconductivity.
For the second class of materials, the goal is to predict signatures of unconventional phases (for example for metallic adatom layers on semiconducting surfaces) and distinguish them from other trivial phases like spin density-waves or conventional superconductivity. Further, we will study impurities on the top of topological superconductors which can reveal the order parameter of an exotic superconductor through the quasiparticle interference pattern or even affect the order parameter itself. While in 3D TIs the unconventional superconductivity is rather ruled by spin-orbit coupling, in the second class of materials it is driven by electron-electron interactions and the lattice symmetry. Therefore this project addresses the fundamental physics question which mechanism leads to a more robust formation of topological superconductivity.
[B03.1] L. Maier, J. B. Oostinga, D. Knott, C. Brüne, P. Virtanen, G. Tkachov, E. M. Hankiewicz, C. Gould, H. Buhmann, and L. W. Molenkamp, Induced Superconductivity in the Three-Dimensional Topological Insulator HgTe, Phys. Rev. Lett. 109, 186806 (2012).
[B03.3] G. Tkachov and E. M. Hankiewicz, Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions, Phys. Rev. B 88, 075401 (2013).