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 mini-gate controlled planar Josephson junctions (JJs) and demonstrate non-Abelian statistics through MBS fusion, detected by charge sensing using a quantum point contact, based on dynamical simulations. The feasibility of preparing, manipulating, and fusing MBS in two-dimensional (2D) systems is supported in our experiments which demonstrate the gate control of topological transition and 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.

Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions

“…The setup is conveniently configurable and can be utilized to create topological and nontopological areas in a JJ by changing the spin–orbit coupling and chemical potential locally ,, as well as controlling the local supercurrent density distribution along the junction. This control can be used to manipulate and move MBSs for braiding and fusion operations in a fashion similar to that of earlier proposals with nanowires , and recently proposed fusion experiments in JJs with local gate-controlled spatial supercurrent distribution . Further, achieving a homogeneous current distribution, which could be done using the minigates, is favorable to ensure that effects such as trivial edge states and band bending do not interfere with the Majorana signatures and manipulation.…”

“…This control can be used to manipulate and move MBSs for braiding and fusion operations in a fashion similar to that of earlier proposals with nanowires 13,17 and recently proposed fusion experiments in JJs with local gate-controlled spatial supercurrent distribution. 18 Further, achieving a homogeneous current distribution, which could be done using the minigates, is favorable to ensure that effects such as trivial edge states and band bending do not interfere with the Majorana signatures and manipulation. Our heterostructure is grown by molecular beam epitaxy on a semi-insulating InP (100) substrate followed by a graded buffer layer.…”

Tunable Planar Josephson Junctions Driven by Time-Dependent Spin-Orbit Coupling

“…However, we expect that our focus only on linearized Rashba SOC, easily tunable by E-field [33,34], already clarifies its important role in JJ dynamics. With changing SOC, there are further opportunities for gate-controlled Majorana states and probing their non-Abelian statistics [77,78] or an added tunability in the implementation of superconducting qubits [3,79,80]. This would extend the previously studied qubit tunability by voltage or flux [3,81] as well as the use of π-phase states for an improved qubit operation [82,83].…”

Out of Equilibrium Majoranas in Interacting Kitaev Chains

“…The fusion process requires a slow adiabatic movement of Majoranas, which can be achieved by applying properly adjusted time-dependent local gates to the topological superconducting wire [15]. The rapid progress in 1D quantum-wires with tunable local gates set-ups [15,17,18], provides a promising platform for creation, movement, and fusion of Majoranas [19].…”

“…In terms of SI units the switching time for V = 0 corresponds to τ /∆ ∼ 0.13ns to 3.9ns (using τ = 36, and ∆ = 180µeV or ∆ = 6µeV as in previous litera-ture [19,29]). This is the time required per gate, which, as example, was five in [19].…”