Hybrid structures of topological materials and superconductors contain rich physics due to the inter- play of superconducting pairing and strong spin-orbit coupling. In the previous funding period of this project, we have put emphasis on a better understanding of transport properties in hybrid structures based on quantum spin Hall insulators. Additionally, we have investigated the unconventional pairing at the two-dimensional (2D) surface of a 3D topological insulator. Furthermore, we have identified a single Majorana bound state as the smallest entity that can experience odd-frequency superconductivity. Recently, we have proposed hybrid structures based on topological insulators as functional building blocks for superconducting spintronics.
In the second funding period, we want to extend this research line in two novel directions. On the one hand, we want to analyze hybrid structures based on Weyl semimetals. Our preliminary results show that we can expect an exciting connection between the chirality of the Weyl nodes and observable features in transport setups. We envision that these research activities can shed light on the emergence of quantum anomalies in Weyl semimetals and allow for novel functional device concepts in superconducting spintronics. In particular, we want to better understand if and how a chirality imbalance can influence transport properties of superconductor hybrid structures based on Weyl semimetals. Additionally, we aim for a thorough analysis of higher-angular momentum pairing in Weyl semimetals and observable consequences thereof.
On the other hand, we plan to investigate hybrid structures based on a constriction in a quantum spin Hall insulator that creates a quantum point contact (QPC). In our recent work, we have demon- strated the presence of odd-frequency pairing in such nanostructures if interactions are weak. Next, we intend to analyze the role of Coulomb interaction in the formation of bound states between the QPC and the superconductor. We presume the emergence of parafermions (the interacting counter- parts of Majorana fermions) in such systems. Our theoretical work should make feasible predictions how to create, manipulate, and detect parafermions in constrictions formed by the helical states of quantum spin Hall nanostructures in proximity to s-wave superconductors. In particular, we want to carefully analyze the Josephson effect in a junction formed by two superconductors connected by a QPC based on helical edge states.