Majorana fermions and parafermions in topological insulators

拓扑绝缘体和拓扑超导体是一类具有间隙体谱和无间隙表面态的新型量子材料。由于拓扑结构的原因，这些表面状态的出现对外部扰动具有显著的鲁棒性。在这个提议中，我们想要发现可行的方法来识别和操纵拓扑绝缘子杂化结构中的马约拉纳费米子和顺介子。马约拉纳费米子和参费米子是出现在拓扑超导体边界态的分数激发态。它们被认为是拓扑量子计算机量子比特的组成部分。我们认为最有希望完成这项任务的系统是一个靠近普通s波超导体的双层量子自旋霍尔绝缘体。在该纳米结构中，我们期望螺旋度、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Basel和w<s:1> rzburg小组在理论技能（Basel：量子计算；w<e:1> rzburg：量子输运）和实验能力（在w<e:1> rzburg）方面很好地互补，在实验室中实际实现了这个具有挑战性的系统。因此，我们有信心，我们将开发创新的想法，在这个联盟中随意产生和控制马约拉纳费米子和准费米子。

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.