Reproducing topological properties with quasi-Majorana states

TL;DR

This paper demonstrates that quasi-Majorana states in superconductor-semiconductor devices can mimic true Majorana signatures, but also identifies key differences and suggests their potential use in braiding and quantum computation.

Contribution

It reveals how quasi-Majorana states replicate Majorana signatures and proposes their controlled coupling as a pathway for braiding in quantum computing.

Findings

Quasi-Majorana states produce zero-bias conductance peaks and $4\pi$ Josephson effects.

Coupling of quasi-Majorana states varies exponentially with magnetic field.

A quantized conductance dip distinguishes true Majorana states.

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.