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Reproducing topological properties with quasiMajorana states
by A. Vuik, B. Nijholt, A. R. Akhmerov, M. Wimmer
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Submission summary
Authors (as registered SciPost users):  Anton Akhmerov · Adriaan Vuik · Michael Wimmer 
Submission information  

Preprint Link:  https://arxiv.org/abs/1806.02801v3 (pdf) 
Date accepted:  20191028 
Date submitted:  20191014 02:00 
Submitted by:  Vuik, Adriaan 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
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.
Published as SciPost Phys. 7, 061 (2019)
List of changes
We thank the referee for the favorable assessment of our manuscript. We have addressed
the requests for minor clarifications raised by the referee:
1.) Indeed, the smoothness requirement is not absolute. We now refer explicitly to
previous works that have found nearzero energy states with potentials involving
kinks or abrupt changes. We have also clarified that it is indeed the smooth potential
slope of the tunnel barrier that is responsible for the appearance of quasiMajorana
states in all of our systems, and that the quantum dot in system Fig. 2(b) serves
only as a probe.
2.) We have now clarified that with "spin" we mean the expectation value of
sigma_x.
Furthermore, note that quasiMajorana states are actually favored by
weak spinorbit interaction, as shown in Fig. 2(c) and (d). For this reason,
we focus on the case of weak spinorbit interaction, where the transverse
part of the spinorbit coupling is of negligible influence. In fact, in the
3D model of Sec. VI we do include the transverse part explicitly. For the weak
spinorbit strengths considered there, quasiMajorana states appear. We have
extended the discussion in this regard in the paper.
3.) We have now clarified that we compare the separation of the quasiMajorana
states to the coherence length \xi. Furthermore, we have added to Fig. 4 the spectrum
corresponding to the wave functions as suggested by the referee.
4.) In relation to the questions raised by the referee, we would like to point out that
Fig. 8 was computed using our microscopic model, i.e. the contributions of abovegap
states are explicitly included. We have clarified this aspect in the text.
Furthermore, we have now added at the end of Section V an extended discussion on how
robust the different features of the conductance shown in Fig. 8 are.
5.) We have clarified that the coupling elements t in Eq. (12) and (14) are in units of sqrt(energy).
With respect to quasiMajoranas allowing for topological operations, we would like to
point out that in Sec. VIII we do discuss the fact that quasiMajoranas themselves are
not topologically protected. To avoid confusion, we have renamed topological quantum
computation with quasiMajorana states to protected quantum computation.
With respect to the occurrence of quasiMajoranas at smaller fields, we have now
added the clarification that this indeed holds for a given chemical potential.