Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States

Abstract

It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding operator that does not commute with the braiding cycles in the absence of tunneling, revealing the non-Abelian nature of MBSs. The time-averaged tunneling current exhibits resonances as a function of the tip voltage with a period that is a direct consequence of the interference between the non-commuting braiding operations. Our work opens up a possibility for utilizing parity non-conserving processes to control non-Abelian states.

Published version: 7 pages, 3 figures + Supplemental material (10 pages, 3 figures)

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Cited by in corpus (7)

• Vortex control in superconducting Corbino geometry networks
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Photonic cross-noise spectroscopy of Majorana bound states
• Realization of the Non-endpoint Majorana Bound States in an Extended Kitaev Chain
• Rotating Majorana Zero Modes in a disk geometry
• Super-Poissonian noise from quasiparticle poisoning in electron transport through a pair of Majorana bound states
• Emergence of multiple zero modes bound to vortices in extended topological Josephson junctions