Majorana fermions and parafermions in topological insulators

拓扑绝缘体和拓扑超导体是一类具有带隙体谱和无带隙表面态的新型量子材料。由于拓扑结构的原因，这些表面态的出现对外界扰动具有显著的鲁棒性。在这个提议中，我们希望找到可行的方法来识别和操纵拓扑绝缘体混合结构中的Majorana费米子和Parafermion。马约拉纳费米子和副费米子是分数激发，出现在拓扑超导体的边界状态。我们已经确定，最有希望完成这项任务的平台是一个双层量子自旋霍尔绝缘体，它靠近一个普通的s波超导体。在该纳米结构中，我们预期螺旋度、层内和层间库仑相互作用、无序和超导有序之间存在复杂的相互作用。参与该项目的巴塞尔和维尔茨堡团队在理论技能（巴塞尔：量子计算;维尔茨堡：量子传输）和实验能力（在维尔茨堡）方面很好地互补，以便在实验室中实际实施这一具有挑战性的系统。因此，我们有信心，我们将开发创新的想法，以产生和控制马约拉纳费米子和副费米子在这个财团内。

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.