With non-Abelian statistics and nonlocal degrees of freedom, Majorana bound states (MBS) are suitable for implementing fault-tolerant topological quantum computing. While the main efforts to realize MBS have focused on one-dimensional systems, it requires delicate parameter tuning and its geometric constraints pose significant challenges for the demonstration of non-Abelian statistics. Building on recent experimental advances in planar Josephson junctions (JJs), we propose how to overcome this obstacle in topological JJs and demonstrate non-Abelian statistics with phase or mini-gate control, detected by charge sensing using quantum point contacts. Our proposals, supported by the experiments, would constitute an important milestone towards topological quantum computing.
The engineering of topological superconducting correlations in quantum devices
holds promises for new schemes of quantum computation. A wide class of systems
expected to exhibit such exotic correlations are based on conductors with strong spinorbit
interaction subject to a strong external magnetic field. Here, we show how these
features can be autonomously induced by using a magnetic texture coupled to any
quasi one dimensional conductor. We study a carbon nanotube with superconducting
contacts in close proximity to a magnetic texture. Transport spectroscopy reveals a
spectrum in which superconducting correlations in the carbon nanotube are deeply
modified by a large spin orbit coupling. We extract a value of about 1.1 meV for this
synthetic spin-orbi, larger than the intrinsic spin orbit energy in many other
platforms. Furthermore, a robust zero energy state, the hallmark of devices hosting
localized Majorana modes, emerges at zero magnetic field. Our findings could be
used for advanced experiments, including microwave spectroscopy and braiding
operations.
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