Hybridization and Fusion of Majorana Bound States in Topological Planar Josephson Junctions

Majorana bound states (MBS) with their nonlocal degrees of freedom and non-Abelian statistics have been viewed as a promising candidate for achieving fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their crucial non-Abelian statistics. The recent discovery of topological planar Josephson Junctions (JJs) provides a new promising platform with a large parameter space and multiple effective control for MBS [1-4]. A significant advantage of JJs is the tunable superconducting phase difference, which acts as an additional knob to control the topological phase [3]. Taking this advantage, we propose a novel platform of non-collinear JJs to manipulate MBS with phase control based on the fabrication of InAs/Al JJs. This adaptable implementation reveals how tuning the superconducting phase difference can generate, hybridize, and fuse multiple MBS pairs. By analyzing the influence of the geometry, gate voltage, and magnetic field, we demonstrate the optimal parameter space for the experimental realization of MBS and their fusion, as an important step toward non-Abelian statistics.

[1] F. Pientka, et. al, PRX 7, 021032 (2017).

[2] M. Dartiailh, et. al, PRL 126, 036802 (2021).

[3] T. Zhou, et. al, PRL 124, 137001 (2020).

[4] T. Zhou, et. al, Nat. Commun. 13, 1738 (2022).