## SciPost Submission Page

# Reproducing topological properties with quasi-Majorana states

### by A. Vuik, B. Nijholt, A. R. Akhmerov, M. Wimmer

### Submission summary

As Contributors: | Anton Akhmerov · Adriaan Vuik |

Arxiv Link: | https://arxiv.org/abs/1806.02801v2 |

Date submitted: | 2019-03-31 |

Submitted by: | Vuik, Adriaan |

Submitted to: | SciPost Physics |

Domain(s): | Theor. & Comp. |

Subject area: | Quantum Physics |

### 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, thereby 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. 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 topological quantum computation.