Superconducting hybrid structures based on quantum spin Hall systems give rise to exciting physics by various means. The reason for this is the interplay between spin-orbit coupling and superconductivity. It is known from non-centrosymmetric superconductors that this very interplay results in unconventional superconductivity with a mixed superconducting order parameter. Therefore, already bulk quantum spin Hall systems in proximity to ordinary s-wave superconductors represent a fruitful playground for engineering unconventional superconductivity by feasible constituents.
The situation becomes even more interesting once the helical edge states of the quantum spin Hall systems are involved. Then, the combination of helicity, superconductivity (S), and ferromagnetism (F) yields Majorana bound states at the interface between the two regions with proximity induced S and F gaps. In this project, the main aim is to theoretically better understand the proximity effect in quantum spin Hall systems and its implication on the detection of unconventional superconductivity as well as the emergence of Majorana bound states. The idea is to identify certain control parameters, for instance, an external magnetic field or a gate voltage that allow us to tune the order parameter of the induced superconductivity. We envision to be able to predict a way to verify the symmetry of the order parameter by transport signatures in normal metal - superconductor (NS) and Josephson (SNS) junctions. This theoretical analysis will be done on the basis of the Bogoliubov - de Gennes formalism.
Furthermore, we want to carefully analyze transport properties of dirty junctions between helical liquids and superconductors. Due to helicity, elastic backscattering off non-magnetic impurities should be forbidden in this system resulting in a so-called perfect Andreev reflection. Therefore, any deviation from perfect Andreev reflection is either coming from magnetic impurities or inelastic backscattering off non-magnetic disorder. We aim to analyze both scattering mechanisms and predict experimental observables, such as the differential conductance, that allow us to identify the most relevant processes. Since inelastic backscattering in these systems is intimately connected to Coulomb interaction within the helical liquids, we plan to employ Tomonaga-Luttinger liquid theory to address this problem.
[B05.6] F. Crepin and B. Trauzettel, Parity measurement in topological Josephson junctions, Phys. Rev. Lett. 112, 077002 (2014).