Fusion of Majorana Bound States with Mini-Gate Control in Two-Dimensional Systems

Abstract

A hallmark of topological superconductivity is the non-Abelian statistics of Majorana bound states (MBS), its chargeless zero-energy emergent quasiparticles. The resulting fractionalization of a single electron, stored nonlocally as a two spatially separated MBS, provides a powerful platform for implementing fault-tolerant topological quantum computing. However, despite intensive efforts, experimental support for MBS remains indirect and does not probe their non-Abelian statistics. Here we propose how to overcome this obstacle in minigate controlled planar Josephson junctions (JJ) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the control of superconducting properties with five mini gates in InAs/Al-based JJs. While we focus on this well-established platform, where the topological superconductivity was already experimentally detected, our proposal to identify elusive non-Abelian statistics motivates also further MBS studies in other gate-controlled 2D systems.

Signatures of Topological Transitions in the Spin Susceptibility of Josephson Junctions

“…Furthermore, it has also been shown that the presence of critical current minima may not necessarily be associated to transitions between the trivial and TS states [45] and a further analysis of magnetic and crystalline anisotropies of the TS state [46,47] may be needed to better understand the physical origin of the critical current minima [36]. In spite of the challenges, planar JJs continue to attract attention due to their experimental feasibility, versatility, and enhanced region of system parameters supporting the TS state [41,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Fusion rules in a Majorana single-charge transistor

“…Just like with braiding, the result is topologically protected and insensitive to the details of the measurement. Different methods have been proposed to demonstrate the MBS fusion rules [33,[46][47][48][49][50][51][52][53].…”