One-dimensional Majorana modes in electronic circuits

该项目致力于凝聚态物质中一维(手征)Majorana模的快速演化和扩展领域。最近通过实验观察到，这些模式出现在二维拓扑超导体的边缘。它们将马约拉纳零模的研究扩展到一个新的、基本上未被探索的方向。将马约拉纳费米子描述为规则狄拉克费米子的一半，在这里得到了一个特别明确的理由。事实上，某些包含狄拉克-马约拉纳和马约拉纳-狄拉克转换器(散射结)的边缘状态网络显示，与只有狄拉克模式的电路中的普通值相比，量子化的电导减半。在这个项目中，我们计划探索电子电路中一维Majorana模的性质，考虑相互作用、无序和量子干扰的影响。具体地说，工作包I致力于在具有1D Majorana模式和相关编织协议的干涉仪中传输。此外，工作包II处理了无序和相互作用对具有反向传播模式的一维Majorana线的影响。最后，在工作包III中，我们将研究在拓扑自旋系统的边缘出现的一维Majorana模(例如，在Kitaev蜂窝模型中)以及使用常规约瑟夫森量子比特实现这种电路。该项目的最终目标是确定Majorana电路相对于相互作用和缺陷的稳定性和保真度，并探索将这些电路用于拓扑量子计算的可能性和具体方法。

This project is devoted to the rapidly evolving and expanding field of one-dimensional (chiral) Majorana modes in condensed matter. These modes, recently observed experimentally, emerge at the edges of two-dimensional topological superconductors. They extend the research of the Majorana zero modes into a new, largely unexplored direction. Characterization of a Majorana fermion as one half of a regular Dirac fermion receives here a particularly clear justification. Indeed, certain networks of edge states containing the Dirac-to-Majorana and Majorana-to-Dirac converters (scattering junctions) show the quantized conductance halved as compared to the usual value in circuits with only Dirac modes. In this project we plan to explore the properties of 1D Majorana modes in electronic circuits, taking into account effects of interactions, disorder, and quantum interference. Specifically, Work Package I is devoted to transport in interferometers with 1D Majorana modes and associated braiding protocols. Further, Work Package II deals with influence of disorder and interactions on 1D Majorana wires with counter-propagating modes. Finally, within Work Package III we will study 1D Majorana modes emerging at edges of topological spin systems (for instance, in the Kitaev honeycomb model) as well as implementation of such circuits using regular Josephson qubits. The ultimate goal of the project is to determine the degree of stability and fidelity of the Majorana circuits with respect to the interactions and imperfections and to explore the possibility and specific approaches to using these circuits for topological quantum computation.