## Reproducing topological properties with quasi-Majorana states

Adriaan Vuik, Bas Nijholt, Anton R. Akhmerov, Michael Wimmer

SciPost Phys. 7, 061 (2019) · published 12 November 2019

- doi: 10.21468/SciPostPhys.7.5.061
- Submissions/Reports

### Abstract

Andreev bound states in hybrid superconductor-semiconductor devices can have near-zero energy in the topologically trivial regime as long as the confinement potential is sufficiently smooth. These quasi-Majorana states show zero-bias conductance features in a topologically trivial phase, mimicking spatially separated topological Majorana states. We show that in addition to the suppressed coupling between the quasi-Majorana states, also the coupling of these states across a tunnel barrier to the outside is exponentially different for increasing magnetic field. As a consequence, quasi-Majorana states mimic most of the proposed Majorana signatures: quantized zero-bias peaks, the $4\pi$ Josephson effect, and the tunneling spectrum in presence of a normal quantum dot. We identify a quantized conductance dip instead of a peak in the open regime as a distinguishing feature of true Majorana states in addition to having a bulk topological transition. Because braiding schemes rely only on the ability to couple to individual Majorana states, the exponential control over coupling strengths allows to also use quasi-Majorana states for braiding. Therefore, while the appearance of quasi-Majorana states complicates the observation of topological Majorana states, it opens an alternative route towards braiding of non-Abelian anyons and protected quantum computation.

### Cited by 26

### Ontology / Topics

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^{1}Adriaan Vuik, -
^{1}Bas Nijholt, -
^{1}Anton Akhmerov, -
^{1}Michael Wimmer