Adriaan Vuik, Bas Nijholt, Anton R. Akhmerov, Michael Wimmer
SciPost Phys. 7, 061 (2019) ·
published 12 November 2019
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· pdf
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.
