Majorana fermions and parafermions in topological insulators

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Topological insulators and topological superconductors constitute a new class of quantum materials with a gapped bulk spectrum and gapless surface states. Due to topology, the appearance of these surface states is remarkably robust against external perturbations.In this proposal, we want to discover feasible ways to identify and manipulate Majorana fermions and parafermions in topological insulator hybrid structures. Majorana fermions and parafermions are fractional excitations that appear as boundary states of topological superconductors. They are known to be building blocks for qubits of a topological quantum computer.The system we have identified as the most promising platform for this task is a bilayer quantum spin Hall insulator in proximity to an ordinary s-wave superconductor. In that nanostructure, we expect a complex interplay between helicity, intra- and inter-layer Coulomb interaction, disorder, and superconducting order. The Basel and Würzburg groups, involved in the project, nicely complement each other in terms of theoretical skills (Basel: quantum computing; Würzburg: quantum transport) and the experimental ability (at Würzburg) to actually implement this challenging system in the laboratory. We are therefore confident that we will develop innovative ideas to generate and control Majorana fermions and parafermions at will within this consortium.