Towards Non-Abelian Statistics in Topological Planar Josephson Junctions*

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. 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 advances in planar Josephson junctions (JJs) [1], we propose a novel platform of X-shaped JJs [2], where phase control can generate, exchange, and braid MBS. The underlying topological superconductivity exists over a large parameter space, consistent with our fabricated materials. With our experimental control of superconducting properties using five mini-gates in InAs/Al-based JJs, we show how such mini-gate control demonstrates non-Abelian statistics through MBS fusion [3], paving a promising way to topological quantum computing.

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

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

[3] T. Zhou, et. al, arXiv: 2101.09272 (2021).