Majorana bound state manipulation by current pulses

Abstract

Majorana bound states (MBSs) can occur in Josephson junctions of conventional s-wave superconductors coupled via a strong topological insulator. In configurations of multiple line junctions meeting at a point, the criterion for the MBS to exist coincides with the presence of a fractional Josephson vortex with 2π phase winding. We investigate the dynamic stability of such vortices in arrays of tri- and quad-junctions. The existence of fractional vortices in arrays is demonstrated, but the dynamic stability is found to depend critically on the current-phase relation and the inductance. We propose the idea, and study the feasibility, of manipulating the location of the vortices in arrays by using current pulses, compatible with rapid single flux quantum technology. It is shown theoretically, using a modified resistively shunted junction model, that braiding operations can be achieved using current pulses injected from the edge of the array. It is necessary to use vortex sites with elevated critical current as traps.

Braiding Operations for a Topological Josephson Junction Array using SFQ Current Pulses

“…Recently, manipulation methods with current pulses for MBS were proposed for topological Josephson junction (JJ) arrays [8]. Via configuration with multiple line junctions meeting at a point, this is equivalent to a schematic of a superconducting loop with multiple junctions, where the criteria for the MBS to exist coincides with the presence of a fractional Josephson vortex with 2π phase winding (2π vortex).…”

“…The existence criterion of 2π vortices depends strongly on the inductance parameter β L = 2πLI c0 /Φ 0 and the percentage of 4π periodic current component α, where Φ 0 is the SFQ. Typical values are reported to be β L = 3.77 and α = 0.2 [8].…”

Dynamic Josephson Vortex Phenomena

“…This is a reprint M. Lankhorst, T. Jansen, A. Brinkman, and A. Golubov, "Majorana bound state manipulation by current pulses," Superconductor science and technology, vol. 34, Feb. (2021)[95].…”