Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires

• Published in: Physical review. B, Condensed matter and materials physics Vol. 94; no. 3
• Main Authors: Hell, Michael, Danon, Jeroen, Flensberg, Karsten, Leijnse, Martin
• Format: Journal Article
• Language: English
• Published: 15-07-2016
• Subjects: Condensed Matter Physics; Den kondenserade materiens fysik; Fysik; Natural Sciences; Naturvetenskap; Physical Sciences
• ISSN: 1098-0121
• DOI: 10.1103/PhysRevB.94.035424

We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating interisland Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently (D. Aasen, arXiv:1511.05153). We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures.