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

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Andreev bound states in hybrid superconductorsemiconductor devices can have
nearzero energy in the topologically trivial regime as long as the confinement
potential is sufficiently smooth. These quasiMajorana states show zerobias
conductance features in a topologically trivial phase, mimicking spatially
separated topological Majorana states. We show that in addition to the
suppressed coupling between the quasiMajorana states, also the coupling of
these states across a tunnel barrier to the outside is exponentially different
for increasing magnetic field. As a consequence, quasiMajorana states mimic
most of the proposed Majorana signatures: quantized zerobias 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 quasiMajorana states for braiding.
Therefore, while the appearance of quasiMajorana states complicates the
observation of topological Majorana states, it opens an alternative route
towards braiding of nonAbelian anyons and protected quantum computation.
M. Istas, C. Groth, A. R. Akhmerov, M. Wimmer, X. Waintal
SciPost Phys. 4, 026 (2018) ·
published 23 May 2018

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We propose a robust and efficient algorithm for computing bound states of
infinite tightbinding systems that are made up of a finite scattering region
connected to semiinfinite leads. Our method uses wave matching in close
analogy to the approaches used to obtain propagating states and scattering
matrices. We show that our algorithm is robust in presence of slowly decaying
bound states where a diagonalization of a finite system would fail. It also
allows to calculate the bound states that can be present in the middle of a
continuous spectrum. We apply our technique to quantum billiards and the
following topological materials: Majorana states in 1D superconducting
nanowires, edge states in the 2D quantum spin Hall phase, and Fermi arcs in 3D
Weyl semimetals.
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