Phase Control of Majorana Bound States in a Topological X Junction*

Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian statistics, they are suitable for implementing fault-tolerant topological quantum computing [1]. While the main efforts to realize MBS have focused on 1D systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experiments in planar Josephson junctions (JJs) [2-4], we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards topological quantum computing.
[1] C. Nayak, et. al, Rev. Mod. Phys. 80, 1083 (2008).
[2] A. Fornieri, et. al, Nature 569, 89 (2019).
[3] H. Ren, et. al, Nature 569, 93 (2019).
[4] W. Mayer, et. al, arXiv:1906.01179 (2019).