One-dimensional Majorana modes in electronic circuits

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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.