One-dimensional Majorana modes in electronic circuits

该项目致力于凝聚态物质中一维（手性）马约拉纳模式的快速发展和扩展领域。这些模式，最近观察到的实验，出现在二维拓扑超导体的边缘。他们将马约拉纳零模的研究扩展到一个新的、基本上未探索的方向。马约拉纳费米子作为正规狄拉克费米子的一半的特征在这里得到了特别明确的证明。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出与仅具有狄拉克模式的电路中的通常值相比减半的量子化电导。在这个项目中，我们计划探索电子电路中1D Majorana模式的特性，同时考虑相互作用，无序和量子干涉的影响。具体来说，工作包I是专门用于运输的干涉仪与1D马约拉纳模式和相关的编织协议。此外，工作包II涉及的影响，无序和相互作用的1D马约拉纳线与反传播模式。最后，在工作包III中，我们将研究拓扑自旋系统边缘出现的1D Majorana模式（例如，Kitaev蜂窝模型）以及使用常规约瑟夫森量子位实现此类电路。该项目的最终目标是确定马约拉纳电路在相互作用和不完美方面的稳定性和保真度，并探索使用这些电路进行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.